A First Book in Algebra
Wallace Clarke Boyden, 1895. Silver, Burdett and Company, 1895
Provenance and licence
Text: Project Gutenberg eBook #13309, released August 27, 2004. The transcription's licence, as it states it:
This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org
This site quotes excerpts and problems from that transcription and hosts no scans; scans are linked to their archive. The records below (problems, checks, errata) are from pd-books at b3c614f, dedicated to the public domain (CC0), export generated 2026-10-10T11:13:12Z.
Chapters
- PREFACE 5 excerpts, 0 equations, 161 problems
- MODES OF REPRESENTING THE OPERATIONS 5 excerpts, 4 equations, 54 problems
- ALGEBRAIC EXPRESSIONS 7 excerpts, 0 equations, 20 problems
- ADDITION 5 excerpts, 0 equations, 28 problems
- SUBTRACTION 5 excerpts, 4 equations, 50 problems
- MULTIPLICATION 5 excerpts, 3 equations, 141 problems
- DIVISION 7 excerpts, 2 equations, 153 problems
- FACTORING 5 excerpts, 8 equations, 224 problems
- GREATEST COMMON FACTOR 4 excerpts, 3 equations, 16 problems
- LEAST COMMON MULTIPLE 3 excerpts, 0 equations, 20 problems
- REDUCTION OF FRACTIONS 5 excerpts, 5 equations, 63 problems
- OPERATIONS UPON FRACTIONS 5 excerpts, 7 equations, 161 problems
- COMPLEX FRACTIONS 3 excerpts, 2 equations, 41 problems
- EQUATIONS 6 excerpts, 2 equations, 171 problems
- SIMULTANEOUS EQUATIONS 9 excerpts, 2 equations, 83 problems
Index of terms 117 terms, by chapter
Related books
The books the concept graph relates to this one, most shared terms first.
- The First Steps in Algebra 1894
101 shared terms
- A Course of Pure Mathematics 1921
19 shared terms
- Calculus Made Easy 1914
18 shared terms
- An Introduction to Mathematics 1911
15 shared terms
- Elementary Illustrations of the Differential and Integral Calculus 1899
15 shared terms
- First Course in the Theory of Equations 1922
13 shared terms
- Mathematical Recreations and Essays 1905
11 shared terms
- Vector Analysis and Quaternions 1906
10 shared terms
- Plane Geometry 1899
4 shared terms
- Treatise on Thermodynamics 1903
2 shared terms
- Solid Geometry with Problems and Applications 1919
1 shared term
- Elements of Plane Trigonometry 1863
0 shared terms recorded.
Errata (65)
G001: Exercise 31, item 15 (Factor), p. 77
Printed: 4x^3 y - 12a x^2 - 8 x y^3
Corrected: 4x^3 y - 12x^2 y^2 - 8 x y^3transcription (a term mis-set in the 2004 transcription; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The book's answer 4xy(x^2-3xy-2y^2) expands to 4x^3y - 12x^2y^2 - 8xy^3, not to the transcription's problem (our answer checker, factor: FLAG-MISMATCH at seeded points). The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett 1894, University of California Libraries), leaf n80, printed page 77, reads "15. 4x^3y - 12x^2y^2 - 8xy^3.", read from the page image (evidence/scan-1894-p77-exercise-31.jpg). The scan is the 1894 printing; the transcription's title page says 1895, same publisher.
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G002: Exercise 15, item 7 (Find the sum of), p. 44
Printed: $5x^2$, $3ab$, $-2ab$, $-4a^2$, $5ab$, $-2a^2$
Corrected: $5x^2$, $3ab$, $-2ab$, $-4x^2$, $5ab$, $-2x^2$transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 44 (leaf n47), reads "7. 5x^2, 3ab, -2ab, -4x^2, 5ab, -2x^2", read from the page image on 2026-10-10. The transcription has -4a^2 and -2a^2 for the page's -4x^2 and -2x^2; the page's x^2 terms sum to -x^2. The page's printed answer, printed page 157 (leaf n160), is "6ab - x^2"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G003: Exercise 15, item 20 (Add), p. 45
Printed: $3a^m - a^{m-1} - 1$, $3a^{m-1} + 1 - 2a^m$, $a^{m-1} + 1$
Corrected: $3a^m - a^{m-1} - 1$, $3a^{m-1} + 1 - 2a^m$, $a^m - 2a^{m-1} + 1$transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 45 (leaf n48), reads "20. 3a^m - a^(m-1) - 1, 3a^(m-1) + 1 - 2a^m, a^m - 2a^(m-1) + 1", read from the page image on 2026-10-10. The transcription dropped "a^m - 2" from the third addend; the printed answer is right. The page's printed answer, printed page 157 (leaf n160), is "2a^m + 1"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G004: Exercise 15, item 25 (Add), p. 45
Printed: a^2b + b^3 - bc^2
Corrected: a^2b + b^3 + bc^2transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 45 (leaf n48), reads item 25 as "second addend: a^2b + b^3 + bc^2 - ab^2 - b^2c - abc (others as transcribed)", read from the page image on 2026-10-10. The transcription has -bc^2 in the second addend where the page prints +bc^2. The page's printed answer, printed page 157 (leaf n160), is "a^3 + b^3 + c^3 - 3abc"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G005: Answers, Exercise 16, answer 8 (subtraction), p. 157
Printed: 9 ax
Corrected: 9 a^2xtranscription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 157 (leaf n160), prints answer 8 of Exercise 16 as "9a^2x", read from the page image on 2026-10-10; the problem, printed page 48 (leaf n51), reads "From the difference between 5a^2x and -3a^2x take the sum of 2a^2x and -3a^2x". The transcription dropped the exponent 2 from the answer. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G006: Exercise 16, item 11 (subtraction), p. 48
Printed: from $11x^{4} - 2x^{3} -
Corrected: from $11x^{4} - 2x^{3} + 3x^{2} -transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 48 (leaf n51), reads "11. Subtract 3x^4 - x^2 + 7x - 14 from 11x^4 - 2x^3 + 3x^2 - 8x", read from the page image on 2026-10-10. The transcription dropped "+3x^2" from the second polynomial; the printed answer is right. The page's printed answer, printed page 157 (leaf n160), is "8x^4 - 2x^3 + 4x^2 - 15x + 14"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G007: Exercise 16, item 26 (subtraction), p. 49
Printed: 5a^2b - 6ab^3 - 7a^2b^2
Corrected: 5a^2b - 6ab^2 - 7a^2b^2transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 49 (leaf n52), reads item 26 as "...and 5a^2b - 6ab^2 - 7a^2b^2... (rest as transcribed)", read from the page image on 2026-10-10. The transcription has 6ab^3 where the page prints 6ab^2. The page's printed answer, printed page 157 (leaf n160), is "-11a^2b + 4ab^2 - 12a^2b^2 - b^3"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G008: Exercise 17, item 7 (Remove the parentheses), p. 51
Printed: a - (3b - 2c + a) - (2b - a - c) - (6 - c + a)
Corrected: a - (3b - 2c + a) - (2b - a - c) - (b - c + a)transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 51 (leaf n54), reads "7. a - (3b - 2c + a) - (2b - a - c) - (b - c + a)", read from the page image on 2026-10-10. The transcription has (6 - c + a) for the page's (b - c + a). The page's printed answer, printed page 158 (leaf n161), is "-6b + 4c"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G009: Answers, Exercise 18, answer 9 (Find the product of), p. 158
Printed: -\frac{2}{9}a^2cx^6y^4
Corrected: -\frac{2}{9}a^2cx^5y^4transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 158 (leaf n161), prints answer 9 of Exercise 18 as "-2/9 a^2cx^5y^4", read from the page image on 2026-10-10; the problem, printed page 54 (leaf n57), reads "1/2 xy, -2/3 cx^2, -2/5 a^2y, and -5/3 x^2y^2". The transcription has x^6 in the answer where the page prints x^5. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G010: Exercise 23, item 2 (Review), p. 61
Printed: Multiply $b^4 - 2b^2$ by $b^4 + 2b^2 - 1$
Corrected: Multiply $b^4 - 2b^2 + 1$ by $b^4 + 2b^2 + 1$transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 61 (leaf n64), reads "2. Multiply b^4 - 2b^2 + 1 by b^4 + 2b^2 + 1", read from the page image on 2026-10-10. Both factors are garbled in the transcription; the page's (b^4 - 1)^2 gives the printed answer. The page's printed answer, printed page 160 (leaf n163), is "b^8 - 2b^4 + 1"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G011: Exercise 24, item 3 (Divide), p. 63
Printed: $27a^3 b^3 c$ by $9ab^2 c$
Corrected: $27a^3 b^2 c$ by $9ab^2 c$transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 63 (leaf n66), reads "3. 27a^3b^2c by 9ab^2c", read from the page image on 2026-10-10. The transcription has b^3 in the dividend where the page prints b^2. The page's printed answer, printed page 160 (leaf n163), is "3a^2"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G012: Exercise 24, item 12 (Divide), p. 63
Printed: $60a^4 bc^{11}$ by $-4ab^2 c^7$
Corrected: $60a^4 bc^{11}$ by $-12a^2 bc^7$transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 63 (leaf n66), reads "12. 60a^4bc^11 by -12a^2bc^7", read from the page image on 2026-10-10. The transcription's divisor is -4ab^2c^7; the page prints -12a^2bc^7. The page's printed answer, printed page 160 (leaf n163), is "-5a^2c^4"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G013: Exercise 24, item 19 (Divide), p. 64
Printed: \div 2x^{3}y^{3}z^{4}
Corrected: \div 2x^{3}y^{2}z^{4}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 64 (leaf n67), reads "19. Simplify (-x^2y^3z^2) x (-x^4y^5z^4) ÷ 2x^3y^2z^4", read from the page image on 2026-10-10. The transcription has y^3 in the divisor where the page prints y^2 (and y^3 in the answer where the page prints y^6: G014). The page's printed answer, printed page 160 (leaf n163), is "1/2 x^3y^6z^2"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G014: Answers, Exercise 24, answer 19 (Divide), p. 160
Printed: \frac{1}{2} x^3 y^3 z^2
Corrected: \frac{1}{2} x^3 y^6 z^2transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 160 (leaf n163), prints answer 19 of Exercise 24 as "1/2 x^3y^6z^2", read from the page image on 2026-10-10; the problem, printed page 64 (leaf n67), reads "Simplify (-x^2y^3z^2) x (-x^4y^5z^4) ÷ 2x^3y^2z^4". The transcription has y^3 in the answer where the page prints y^6 (and y^3 in the divisor where the page prints y^2: G013). The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G015: Answers, Exercise 25, answer 7 (Divide), p. 160
Printed: -4y^3 z^3 + 3x^2 y^3 z^4 - xy
Corrected: -4y^3 z^6 + 3x^2 y^3 z^4 - xytranscription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 160 (leaf n163), prints answer 7 of Exercise 25 as "-4y^3z^6 + 3x^2y^3z^4 - xy", read from the page image on 2026-10-10; the problem, printed page 64 (leaf n67), reads "32x^3y^4z^6 - 24x^5y^4z^4 + 8x^4y^2 by -8x^3y". The transcription has z^3 in the answer's first term where the page prints z^6. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G016: Answers, Exercise 26, answer 10 (Divide), p. 161
Printed: 27x^5 + 9x^4y + 3x^2y^2 + y^3
Corrected: 27x^6 + 9x^4y + 3x^2y^2 + y^3transcription (low confidence: a damaged character on the 1894 page, most likely a 6; the 2004 transcription reads 5)
Probable: found by computation; not yet read against a scan.
Status: probable (the scan's character is damaged; read as a 6 by its shape and the book's own algebra). LOW CONFIDENCE. In the rich scan the first exponent of the answer is a broken, poorly inked character, open on the left; it lacks the flat top stroke of the other 5s on the page, and its shape matches the exponent in 26.18, which must be a 6. Two other 1894 copies split: afirstbookinalg00boydgoog (p.161) shows a closed 6, firstbookinalge00boydgoog shows the same broken 5-like shape. Most likely a damaged 6 that the transcriber read as 5; the page reading used here (27x^6) is that interpretation, not a clean reading. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 161 (leaf n164), prints answer 10 of Exercise 26 as "27x^[damaged] + 9x^4y + 3x^2y^2 + y^3", read from the page image on 2026-10-10; the problem, printed page 67 (leaf n70), reads "81x^8 - y^4 by 3x^2 - y". The transcription has 27x^5; the mathematics needs 27x^6. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G017: Exercise 26, item 12 (Divide), p. 67
Printed: $a^5+a^4b-14a^3b^2+15a^2b^3-4b^3$ by $a^2-3ab+2b^2$
Corrected: $a^5+a^4b-13a^3b^2+15a^2b^3-4b^5$ by $a^2-3ab+2b^2$transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 67 (leaf n70), reads "12. a^5 + a^4b - 13a^3b^2 + 15a^2b^3 - 4b^5 by a^2 - 3ab + 2b^2", read from the page image on 2026-10-10. Two figures differ in the transcription's dividend (-14a^3b^2 for the page's -13a^3b^2, -4b^3 for -4b^5); multiplying out the page's answer and divisor gives the page's dividend exactly. The page's printed answer, printed page 161 (leaf n164), is "a^3 + 4a^2b - 3ab^2 - 2b^3"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G018: Exercise 26, item 19 (Divide), p. 68
Printed: $x^4 + 4y^4$ by $x^2 - 2xy + y^2$
Corrected: $x^4 + 4y^4$ by $x^2 - 2xy + 2y^2$transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 68 (leaf n71), reads "19. x^4 + 4y^4 by x^2 - 2xy + 2y^2", read from the page image on 2026-10-10. The transcription's divisor has y^2 where the page prints 2y^2. The page's printed answer, printed page 161 (leaf n164), is "x^2 + 2xy + 2y^2"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G019: Exercise 27, item 17 (Simplify), p. 70
Printed: \sqrt[5]{\frac{32}{243} a^{10} b^{15}}
Corrected: \sqrt[5]{-\frac{32}{243} a^{10} b^{15}}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 70 (leaf n73), reads "17. sqrt(1/9 a^4b^6) - cbrt(1/8 a^6b^9) - 5th-root(-32/243 a^10b^15) + cbrt(a^6b^9)", read from the page image on 2026-10-10. The transcription dropped the minus inside the fifth root; 1/3 - 1/2 + 2/3 + 1 = 3/2. The page's printed answer, printed page 161 (leaf n164), is "3/2 a^2b^3"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G020: Answers, Exercise 33, answer 6 (Factor), p. 163
Printed: (xy^2z^2 + cdm^2)(x^2y^2z^2 - cdm^2)
Corrected: (xy^2z^2 + cdm^2)(xy^2z^2 - cdm^2)transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 6 of Exercise 33 as "(xy^2z^2 + cdm^2)(xy^2z^2 - cdm^2)", read from the page image on 2026-10-10; the problem, printed page 79 (leaf n82), reads "x^2y^4z^4 - c^2d^2m^4". The transcription has x^2y^2z^2 in the second factor. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G021: Answers, Exercise 33, answer 11 (Factor), p. 163
Printed: (9xy^2 - 5bd)(9xy^2 - 5bd)
Corrected: (9xy^2 + 5bd)(9xy^2 - 5bd)transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 11 of Exercise 33 as "(9xy^2 + 5bd)(9xy^2 - 5bd)", read from the page image on 2026-10-10; the problem, printed page 79 (leaf n82), reads "81x^2y^4 - 25b^2d^2". The transcription has a minus in both factors. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G022: Exercise 33, item 16 (Factor), p. 80
Printed: a^4b^8 - l
Corrected: a^8b^8 - 1transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 80 (leaf n83), reads "16. a^8b^8 - 1", read from the page image on 2026-10-10. The transcription has a^4b^8 - l (the letter l) for the page's a^8b^8 - 1. The page's printed answer, printed page 163 (leaf n166), is "(a^4b^4+1)(a^2b^2+1)(ab+1)(ab-1)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G023: Exercise 33, item 19 (Factor), p. 80
Printed: a^4 - ax^2
Corrected: a^3 - ax^2transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 80 (leaf n83), reads "19. a^3 - ax^2", read from the page image on 2026-10-10. The transcription has a^4 for the page's a^3. The page's printed answer, printed page 163 (leaf n166), is "a(a + x)(a - x)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G024: Answers, Exercise 33, answer 22 (Factor), p. 163
Printed: 5a(a + y)(1 + a)(1 - a)
Corrected: 5a(x + y)(1 + a)(1 - a)transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 22 of Exercise 33 as "5a(x + y)(1 + a)(1 - a)", read from the page image on 2026-10-10; the problem, printed page 80 (leaf n83), reads "5ax - 5a^3x + 5ay - 5a^3y". The transcription has (a + y) for the page's (x + y). The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G025: Answers, Exercise 33, answer 24 (Factor), p. 163
Printed: (a - x + 1)(a + x)
Corrected: (a - x - 1)(a + x)transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 24 of Exercise 33 as "(a - x - 1)(a + x)", read from the page image on 2026-10-10; the problem, printed page 80 (leaf n83), reads "a^2 - x^2 - a - x". The transcription has (a - x + 1) for the page's (a - x - 1). The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G026: Exercise 34, item 1 (Factor), p. 81
Printed: x^5 + y^5
Corrected: x^3 + y^3transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 81 (leaf n84), reads "1. x^3 + y^3", read from the page image on 2026-10-10. The transcription has x^5 + y^5 for the page's x^3 + y^3. The page's printed answer, printed page 163 (leaf n166), is "(x + y)(x^2 - xy + y^2)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G027: Exercise 34, item 5 (Factor), p. 81
Printed: 8a^5b^3c^6 + m^6
Corrected: 8a^3b^3c^6 + m^6transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 81 (leaf n84), reads "5. 8a^3b^3c^6 + m^6", read from the page image on 2026-10-10. The transcription has 8a^5 for the page's 8a^3. The page's printed answer, printed page 163 (leaf n166), is "(2abc^2 + m^2)(4a^2b^2c^4 - 2abc^2m^2 + m^4)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G028: Exercise 34, item 6 (Factor), p. 81
Printed: x^6y^3 + 216a^3
Corrected: x^6y^9 + 216a^3transcription (the 2004 transcription mis-set the problem; the book's problem is right, its answer is not: F004)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 81 (leaf n84), reads "6. x^6y^9 + 216a^3", read from the page image on 2026-10-10. The transcription has x^6y^3 for the page's x^6y^9. The page's printed answer, printed page 163 (leaf n166), is "(x^2y^3 + 6a)(x^4y^3 - 6ax^2y^3 + 36a^2)"; it is itself misprinted (F004), and the page's problem gives the corrected answer while the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G029: Exercise 34, item 12 (Factor), p. 81
Printed: 1 + b^3c^3
Corrected: 1 + b^3c^9transcription (the 2004 transcription mis-set the problem; the book's problem is right, its answer is not: F005)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 81 (leaf n84), reads "12. 1 + b^3c^9", read from the page image on 2026-10-10. The transcription has c^3 for the page's c^9. The page's printed answer, printed page 163 (leaf n166), is "(1 + bc^3)(1 - bc^3 + b^2c^5)"; it is itself misprinted (F005), and the page's problem gives the corrected answer while the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G030: Exercise 34, item 13 (Factor), p. 81
Printed: \frac{1}{8}a^6b^3+ c^0
Corrected: \frac{1}{8}a^6b^3+ c^9transcription (the 2004 transcription mis-set the problem; the book's problem is right, its answer is not: F006)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 81 (leaf n84), reads "13. 1/8 a^6b^3 + c^9", read from the page image on 2026-10-10. The transcription has c^0 for the page's c^9. The page's printed answer, printed page 163 (leaf n166), is "(1/2 a^2b + c^3)(1/4 a^4b^2 - 1/2 a^2bc^3 + c^5)"; it is itself misprinted (F006), and the page's problem gives the corrected answer while the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G031: Answers, Exercise 34, answer 14 (Factor), p. 163
Printed: (\frac{1}{4}x + 1)(\frac{1}{2}x^2 - \frac{1}{4}x + 1)
Corrected: (\frac{1}{3}x + 1)(\frac{1}{9}x^2 - \frac{1}{3}x + 1)transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 14 of Exercise 34 as "(1/3 x + 1)(1/9 x^2 - 1/3 x + 1)", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads "1/27 x^3 + 1". The transcription has 1/4, 1/2, 1/4 for the page's 1/3, 1/9, 1/3. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G032: Answers, Exercise 34, answer 16 (Factor), p. 164
Printed: (1 - x - y)\{1 - (x - y) + (x - y)^2\}
Corrected: (1 + x - y)\{1 - (x - y) + (x - y)^2\}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 164 (leaf n167), prints answer 16 of Exercise 34 as "(1 + x - y){1 - (x - y) + (x - y)^2}", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads "1 + (x - y)^3". The transcription has (1 - x - y) for the page's (1 + x - y). The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G033: Answers, Exercise 35, answer 8 (Factor), p. 164
Printed: 4a^2m^4x^4
Corrected: 4a^3m^4x^4transcription (the 2004 transcription departs from the 1894 page, which is itself wrong here: F008)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 164 (leaf n167), prints answer 8 of Exercise 35 as "27(bc^2y - 2a^3m^2x^2)(b^2c^4y^2 + 2a^3bc^2m^2x^2y + 4a^3m^4x^4)", read from the page image on 2026-10-10; the problem, printed page 82 (leaf n85), reads "27b^3c^6y^3 - 216a^9m^6x^6". The transcription has 4a^2 in the last term where the page prints 4a^3 (faint, but shaped like a 3, and not a 2). The page is itself wrong here: the problem needs a^6, not the page's a^3 (F008); this entry records only where the transcription departs from the page. The printed exponent is faint, a 3 or a 5; the claim is only that the page does not print the required 6 (the sympy check rejects both readings).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G034: Answers, Exercise 36, answer 17 (Factor), p. 165
Printed: \left(4xy^2-3a^8\right)^2
Corrected: \left(4xy^2-3a^3\right)^2transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 165 (leaf n168), prints answer 17 of Exercise 36 as "(4xy^2 - 3a^3)^2", read from the page image on 2026-10-10; the problem, printed page 84 (leaf n87), reads "16x^2y^4 - 24a^3xy^2 + 9a^6". The transcription has 3a^8 for the page's 3a^3. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G035: Exercise 36, item 20 (Factor), p. 84
Printed: \frac{1}{9}x^4 - \frac{2}{3}x^2y^2 + 4y^4
Corrected: \frac{1}{9}x^4 - \frac{2}{3}x^2y^2 + y^4transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 84 (leaf n87), reads "20. 1/9 x^4 - 2/3 x^2y^2 + y^4", read from the page image on 2026-10-10. The transcription has 4y^4 for the page's y^4. The page's printed answer, printed page 165 (leaf n168), is "(1/3 x^2 - y^2)^2"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G036: Answers, Exercise 38, answer 5 (Review: Expand), p. 166
Printed: x^6y^3 - 12x^4y^2z^3a^4 + 48x^2yz^8a^8 - 64z^9a^{12}
Corrected: x^6y^3 - 12x^4y^2z^3a^4 + 48x^2yz^6a^8 - 64z^9a^{12}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 166 (leaf n169), prints answer 5 of Exercise 38 as "x^6y^3 - 12x^4y^2z^3a^4 + 48x^2yz^6a^8 - 64z^9a^12", read from the page image on 2026-10-10; the problem, printed page 87 (leaf n90), reads "Expand (x^2y - 4z^3a^4)^3". The transcription has z^8 in the third term for the page's z^6. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G037: Exercise 42, item 3 (Reduce to lowest terms), p. 94
Printed: \frac{x^2-7x+12}{x^3+x-20}
Corrected: \frac{x^2-7x+12}{x^2+x-20}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 94 (leaf n97), reads "3. (x^2 - 7x + 12)/(x^2 + x - 20)", read from the page image on 2026-10-10. The transcription has x^3 in the denominator for the page's x^2. The page's printed answer, printed page 167 (leaf n170), is "(x - 3)/(x + 5)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G038: Exercise 43, item 3 (Change to equivalent entire or mixed numbers), p. 97
Printed: \frac{x^2 + y^2 + 3}{x - y}
Corrected: \frac{x^2 - y^2 + 3}{x - y}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 97 (leaf n100), reads "3. (x^2 - y^2 + 3)/(x - y)", read from the page image on 2026-10-10. The transcription has x^2 + y^2 for the page's x^2 - y^2. The page's printed answer, printed page 167 (leaf n170), is "x + y + 3/(x - y)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G039: Exercise 43, item 4 (Change to equivalent entire or mixed numbers), p. 97
Printed: \frac{a^3 + b^3 + 3}{x - y}
Corrected: \frac{a^3 + b^3 - 2}{a + b}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 97 (leaf n100), reads "4. (a^3 + b^3 - 2)/(a + b)", read from the page image on 2026-10-10. The transcription has (a^3 + b^3 + 3)/(x - y), the numerator's 3 and the denominator apparently carried over from the item above. The page's printed answer, printed page 167 (leaf n170), is "a^2 - ab + b^2 - 2/(a + b)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G040: Exercise 43, item 25 (Change to equivalent fractions), p. 98
Printed: \frac{3x + 2}{x^2 + x + 2} - 1
Corrected: \frac{3x + 2}{x^2 - x + 2} - 1transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 98 (leaf n101), reads "25. (3x + 2)/(x^2 - x + 2) - 1", read from the page image on 2026-10-10. The transcription has x^2 + x + 2 in the denominator for the page's x^2 - x + 2. The page's printed answer, printed page 167 (leaf n170), is "(4x - x^2)/(x^2 - x + 2)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G041: Exercise 44, item 3 (Find the value of), p. 100
Printed: \frac{2x}{3}-\frac{3x}{4}-\frac{4x}{5}
Corrected: \frac{2x}{3}-\frac{3x}{4}+\frac{4x}{5}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 100 (leaf n103), reads "3. 2x/3 - 3x/4 + 4x/5", read from the page image on 2026-10-10. The transcription has - 4x/5 for the page's + 4x/5. The page's printed answer, printed page 168 (leaf n171), is "43x/60"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G042: Exercise 44, item 4 (Find the value of), p. 100
Printed: \frac{4a}{b}+\frac{3x}{2m}
Corrected: \frac{2a}{b}+\frac{3x}{2m}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 100 (leaf n103), reads "4. 2a/b + 3x/2m", read from the page image on 2026-10-10. The transcription has 4a/b for the page's 2a/b. The page's printed answer, printed page 168 (leaf n171), is "(4am + 3bx)/(2bm)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G043: Exercise 44, item 19 (Find the value of), p. 101
Printed: 1} - \frac{3x^3 + 3x^2 - x - 1}
Corrected: 1} + \frac{3x^3 + 3x^2 - x - 1}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 101 (leaf n104), reads "19. (3x^3-3x^2+x-1)/(3x^3-3x^2-x+1) + (3x^3+3x^2-x-1)/(3x^3+3x^2+x+1)", read from the page image on 2026-10-10. The transcription has a minus between the fractions; the page prints +. The page's printed answer, printed page 168 (leaf n171), is "2(9x^4 + 1)/(9x^4 - 1)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G044: Exercise 45, item 4 (Find the value of), p. 105
Printed: \frac{20a-4}{4a^2-1}+\frac{3}{1-2a}-\frac{6}{1-2a}
Corrected: \frac{20a-4}{4a^2-1}+\frac{3}{1-2a}-\frac{6}{1+2a}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 105 (leaf n108), reads "4. (20a - 4)/(4a^2 - 1) + 3/(1 - 2a) - 6/(1 + 2a)", read from the page image on 2026-10-10. The transcription has 6/(1 - 2a) for the page's 6/(1 + 2a). The page's printed answer, printed page 168 (leaf n171), is "1/(2a + 1)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G045: Exercise 45, item 5 (Find the value of), p. 105
Printed: \frac{3y^3}{y^3-x^3}
Corrected: \frac{3y^2}{y^3-x^3}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 105 (leaf n108), reads "5. 1/(x - y) + 3y^2/(y^3 - x^3) - (x - y)/(x^2 + xy + y^2)", read from the page image on 2026-10-10. The transcription has 3y^3 in the second numerator for the page's 3y^2 (one of two slips in this item: G046). The page's printed answer, printed page 168 (leaf n171), is "3y/(x^2 + xy + y^2)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G046: Exercise 45, item 5 (Find the value of), p. 105
Printed: - \frac{1}{3(1+a)}
Corrected: - \frac{x-y}{x^2+xy+y^2}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 105 (leaf n108), reads "5. 1/(x - y) + 3y^2/(y^3 - x^3) - (x - y)/(x^2 + xy + y^2)", read from the page image on 2026-10-10. The transcription's third term is garbled, 1/(3(1+a)) for the page's (x - y)/(x^2 + xy + y^2) (one of two slips in this item: G045). The page's printed answer, printed page 168 (leaf n171), is "3y/(x^2 + xy + y^2)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G047: Exercise 49, item 4 (Simplify), p. 110
Printed: \frac{3a^3mn^2}{2x^3yz^2}
Corrected: \frac{3a^3mn^2}{2xy^3z^2}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 110 (leaf n113), reads "4. 2am^3n^2/(3x^3yz^2) ÷ 3a^3mn^2/(2xy^3z^2)", read from the page image on 2026-10-10. The transcription has 2x^3yz^2 in the divisor's denominator for the page's 2xy^3z^2. The page's printed answer, printed page 170 (leaf n173), is "4m^2y^2/(9a^2x^2)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G048: Answers, Exercise 50, answer 2 (Find by inspection the values), p. 170
Printed: \frac{a^3b^9}{64y^3}
Corrected: \frac{a^6b^9}{64y^3}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 170 (leaf n173), prints answer 2 of Exercise 50 as "a^6b^9/(64y^3)", read from the page image on 2026-10-10; the problem, printed page 112 (leaf n115), reads "(a^2b^3/4y)^3". The transcription has a^3 in the answer for the page's a^6. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G049: Answers, Exercise 50, answer 5 (Find by inspection the values), p. 170
Printed: -\frac{125x^5y^3\left(a+b^2\right)^6}
Corrected: -\frac{125x^6y^3\left(a+b^2\right)^6}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 170 (leaf n173), prints answer 5 of Exercise 50 as "-125x^6y^3(a+b^2)^6 / 8a^3b^9(x^2-y)^9", read from the page image on 2026-10-10; the problem, printed page 112 (leaf n115), reads "(-5x^2y(a+b^2)^2 / 2ab^3(x^2-y)^3)^3". The transcription has x^5 in the answer for the page's x^6. The page's problem gives the page's answer, not the transcription's (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G050: Exercise 50, item 6 (Find by inspection the values), p. 112
Printed: \frac{3am^4(2a+3b)^3}{4x^2y^2(m-n)^2}
Corrected: \frac{3am^4(2a+3b)^3}{4x^2y^3(m-n)^2}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 112 (leaf n115), reads "6. (-3am^4(2a+3b)^3 / 4x^2y^3(m-n)^2)^3", read from the page image on 2026-10-10. The transcription has y^2 in the problem for the page's y^3, so the answer's y^9 is correct. The page's printed answer, printed page 170 (leaf n173), is "-27a^3m^12(2a+3b)^9 / 64x^6y^9(m-n)^6"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G051: Exercise 50, item 19 (Find by inspection the values), p. 113
Printed: \frac{x^2}{2mn}
Corrected: \frac{x^2y}{2mn}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 113 (leaf n116), reads "19. 3ab(2x/ab + x^2y/2mn - ax/3mb)", read from the page image on 2026-10-10. The transcription dropped the y from the problem's second term, not from the answer. The page's printed answer, printed page 170 (leaf n173), is "6x + 3abx^2y/(2mn) - a^2x/m"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G052: Exercise 50, item 22 (Find by inspection the values), p. 113
Printed: \frac{9y^2}{25m^1}
Corrected: \frac{9y^2}{25m^2}transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 113 (leaf n116), reads "22. (x^2/16 + 9y^2/25m^2)(x/4 + 3y/5m)(x/4 - 3y/5m)", read from the page image on 2026-10-10. The transcription has m^1 for the page's m^2. The page's printed answer, printed page 170 (leaf n173), is "x^4/256 - 81y^4/(625m^4)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
G053: Exercise 50, item 25 (Find by inspection the values), p. 113
Printed: \frac{3a^2}{2b} \right)$
Corrected: \frac{3a^2}{2b} \right)^2$transcription (the 2004 transcription departs from the 1894 page; the book is right)
Confirmed against a scan of the printed book: the transcription differs, the book is right.
Status: confirmed against a scan. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 113 (leaf n116), reads "25. (x/y - 3a^2/2b)^2", read from the page image on 2026-10-10. The transcription dropped the square from the problem. The page's printed answer, printed page 170 (leaf n173), is "x^2/y^2 - 3a^2x/(by) + 9a^4/(4b^2)"; the page's problem gives it and the transcription's problem does not (sympy check in boyden_found.py).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F001: Answers, Exercise 15, answer 22 (Add), p. 157
Printed: 23x^3 - 20x^2 + 27x + 6
Corrected: 23x^3 + 20x^2 + 27x + 6content (sign): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 157 (leaf n160), prints answer 22 of Exercise 15 as "23x^3 - 20x^2 + 27x + 6", read from the page image on 2026-10-10; the problem, printed page 45 (leaf n48), reads "22. 15x^3 + 35x^2 + 3x + 7, 7x^3 + 15x - 11x^2 + 9, 9x - 10 + x^3 - 4x^2". 35 - 11 - 4 = +20, so the sum's x^2 term is +20x^2; the page prints -20x^2. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here.
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F002: Answers, Exercise 19, answer 11 (Multiply), p. 158
Printed: a^6 + b^6
Corrected: a^6 - b^6content (sign): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 158 (leaf n161), prints answer 11 of Exercise 19 as "a^6 + b^6", read from the page image on 2026-10-10; the problem, printed page 56 (leaf n59), reads "11. a^5 - a^4b + a^3b^2 - a^2b^3 + ab^4 - b^5 by a + b". (a + b)(a^5 - a^4b + a^3b^2 - a^2b^3 + ab^4 - b^5) = a^6 - b^6; the page prints a^6 + b^6. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here. The rich scan has a faint grey smudge over the sign, but the + strokes are clear; two other 1894 copies (Google scans afirstbookinalg00boydgoog p.158 and firstbookinalge00boydgoog) also print a clean +.
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F003: Answers, Exercise 33, answer 5 (Factor), p. 163
Printed: (a^3bx^2 + m^2c^4y^{10})(a^3bx^2 - m^2c^4y^{10})
Corrected: (a^3bx^2 + m^2c^4y^5)(a^3bx^2 - m^2c^4y^5)content (exponent): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 5 of Exercise 33 as "(a^3bx^2 + m^2c^4y^10)(a^3bx^2 - m^2c^4y^10)", read from the page image on 2026-10-10; the problem, printed page 79 (leaf n82), reads "5. a^6b^2x^4 - m^4c^8y^10". a^6b^2x^4 - m^4c^8y^10 = (a^3bx^2)^2 - (m^2c^4y^5)^2, so both factors need y^5; the page prints y^10 in each. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here. A reader of this copy pencilled "5" over both 10s.
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F004: Answers, Exercise 34, answer 6 (Factor), p. 163
Printed: (x^2y^3 + 6a)(x^4y^3 - 6ax^2y^3 + 36a^2)
Corrected: (x^2y^3 + 6a)(x^4y^6 - 6ax^2y^3 + 36a^2)content (exponent): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 6 of Exercise 34 as "(x^2y^3 + 6a)(x^4y^3 - 6ax^2y^3 + 36a^2)", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads "6. x^6y^9 + 216a^3". (x^2y^3 + 6a)(x^4y^6 - 6ax^2y^3 + 36a^2) = x^6y^9 + 216a^3; the page prints y^3 for y^6 in the second factor. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The 2004 transcription silently has the correct y^6 here (13309-t.tex line 8152), so printed above is what the page prints, written in the transcription's notation, and corrected is the transcription as it stands. The transcription also mis-sets this problem (G028).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F005: Answers, Exercise 34, answer 12 (Factor), p. 163
Printed: (1 + bc^3)(1 - bc^3 + b^2c^5)
Corrected: (1 + bc^3)(1 - bc^3 + b^2c^6)content (exponent): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 12 of Exercise 34 as "(1 + bc^3)(1 - bc^3 + b^2c^5)", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads "12. 1 + b^3c^9". 1 + b^3c^9 = (1 + bc^3)(1 - bc^3 + b^2c^6); the page prints c^5. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here. The transcription also mis-sets this problem (G029). The printed exponent is faint, a 3 or a 5; the claim is only that the page does not print the required 6 (the sympy check rejects both readings).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F006: Answers, Exercise 34, answer 13 (Factor), p. 163
Printed: - \frac{1}{2}a^2bc^3 + c^5)
Corrected: - \frac{1}{2}a^2bc^3 + c^6)content (exponent): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 163 (leaf n166), prints answer 13 of Exercise 34 as "(1/2 a^2b + c^3)(1/4 a^4b^2 - 1/2 a^2bc^3 + c^5)", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads "13. 1/8 a^6b^3 + c^9". 1/8 a^6b^3 + c^9 = (1/2 a^2b + c^3)(1/4 a^4b^2 - 1/2 a^2bc^3 + c^6); the page prints c^5. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here. The transcription also mis-sets this problem (G030). The printed exponent is faint, a 3 or a 5; the claim is only that the page does not print the required 6 (the sympy check rejects both readings).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F007: Answers, Exercise 34, answer 21 (Factor), p. 164
Printed: (27x^3 + 4y^3)(27x^3 - 4y^3)
Corrected: (27x^3 + 8y^3)(27x^3 - 8y^3)content (coefficient): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 164 (leaf n167), prints answer 21 of Exercise 34 as "(27x^3 + 4y^3)(27x^3 - 4y^3)", read from the page image on 2026-10-10; the problem, printed page 81 (leaf n84), reads "21. 729x^6 - 64y^6". 729x^6 - 64y^6 = (27x^3)^2 - (8y^3)^2; the page prints 4y^3. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here. The 4 is clear both times.
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F008: Answers, Exercise 35, answer 8 (Factor), p. 164
Printed: 4a^3m^4x^4
Corrected: 4a^6m^4x^4content (exponent): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 164 (leaf n167), prints answer 8 of Exercise 35 as "27(bc^2y - 2a^3m^2x^2)(b^2c^4y^2 + 2a^3bc^2m^2x^2y + 4a^3m^4x^4)", read from the page image on 2026-10-10; the problem, printed page 82 (leaf n85), reads "8. 27b^3c^6y^3 - 216a^9m^6x^6". 27(bc^2y - 2a^3m^2x^2)(b^2c^4y^2 + 2a^3bc^2m^2x^2y + 4a^6m^4x^4) = 27b^3c^6y^3 - 216a^9m^6x^6; the page prints a^3 in the last term. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The 2004 transcription has 4a^2m^4x^4 here (13309-t.tex line 8206; G033), so printed above is what the page prints, written in the transcription's notation, not the text of 13309-t.tex. The printed exponent is faint, a 3 or a 5; the claim is only that the page does not print the required 6 (the sympy check rejects both readings).
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F009: Answers, Exercise 35, answer 15 (Factor), p. 164
Printed: (\frac{1}{3}xy^2 - b^3)(\frac{1}{9}x^3y^4 + \frac{1}{3}xy^2b^3 + b^6)
Corrected: (\frac{1}{3}xy^2 - b^3)(\frac{1}{9}x^2y^4 + \frac{1}{3}xy^2b^3 + b^6)content (exponent): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 164 (leaf n167), prints answer 15 of Exercise 35 as "(1/3 xy^2 - b^3)(1/9 x^3y^4 + 1/3 xy^2b^3 + b^6)", read from the page image on 2026-10-10; the problem, printed page 82 (leaf n85), reads "15. 1/27 x^3y^6 - b^9". (1/3 xy^2)^2 = 1/9 x^2y^4, so the second factor begins 1/9 x^2y^4; the page prints 1/9 x^3y^4. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here.
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F010: Answers, Exercise 48, answer 2 (Simplify), p. 169
Printed: \frac{2}{3}
Corrected: \frac{3}{4}content (value): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 169 (leaf n172), prints answer 2 of Exercise 48 as "2/3", read from the page image on 2026-10-10; the problem, printed page 109 (leaf n112), reads "2. 9a^2b^2/(8nx^3y^2) x 5x^2y^2/(2am^2n) x 24m^2n^2x/(90ab^2)". (9 x 5 x 24)/(8 x 2 x 90) = 1080/1440 = 3/4, and every letter cancels; the page prints 2/3. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here.
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F011: Answers, Exercise 49, answer 2 (Simplify), p. 170
Printed: \frac{21ab^2y^2}{16mnz^3}
Corrected: \frac{21a^2b^2y^2}{16mnz^3}content (exponent): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 170 (leaf n173), prints answer 2 of Exercise 49 as "21ab^2y^2/(16mnz^3)", read from the page image on 2026-10-10; the problem, printed page 110 (leaf n113), reads "2. 7axy^2/(8m^2n) ÷ 2xz^3/(3ab^2m)". 7axy^2/(8m^2n) x 3ab^2m/(2xz^3) = 21a^2b^2y^2/(16mnz^3); the page prints 21ab^2y^2. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here.
Scan: https://archive.org/details/firstbookinalgeb00boydrich
F012: Answers, Exercise 50, answer 35 (Factor), p. 171
Printed: \left(\frac{m}{y}-5\right)\left(\frac{m}{y}+3\right)
Corrected: \left(\frac{m}{y}+5\right)\left(\frac{m}{y}-3\right)content (sign): the book's own error; the 1894 page prints it
Confirmed: found by computation and read against the printed page.
Status: confirmed against a scan. The 1894 page prints it. The Internet Archive scan firstbookinalgeb00boydrich (Silver, Burdett and Company, 1894), printed page 171 (leaf n174), prints answer 35 of Exercise 50 as "(m/y - 5)(m/y + 3)", read from the page image on 2026-10-10; the problem, printed page 114 (leaf n117), reads "35. m^2/y^2 + 2m/y - 15". (m/y + 5)(m/y - 3) = m^2/y^2 + 2m/y - 15; the printed (m/y - 5)(m/y + 3) gives -2m/y. Checked with sympy in boyden_found.py: the page's problem does not give the printed answer and does give the corrected one. The transcription follows the page here.
Scan: https://archive.org/details/firstbookinalgeb00boydrich