ADDITION

Exercise 15

1. Exercise 15, problem 1

   $3x$, $5x$, $x$, $4x$, $11x$.

   Printed answer:

   • $24x$.

   verified: the printed answer passed a computed check

   How it was checked

   • identity: passes 24*x

2. Exercise 15, problem 10

   $x^5 + 5a^4b - 7ab - 2x^5 + 10ab + 3a^4b$.

   Printed answer:

   • $8a^4b + 3ab - x^5$.

   verified: the printed answer passed a computed check

   How it was checked

   • identity: passes 8*a**4*b + 3*a*b - x**5

3. Exercise 15, problem 11

   $\frac{1}{3}a - \frac{1}{2}a + \frac{2}{3}a + a$.

   Printed answer:

   • $\frac{3}{2}a$.

   verified: the printed answer passed a computed check

   How it was checked

   • identity: passes Rational(3,2)*a

4. Exercise 15, problem 12

   $\frac{2}{3}b - \frac{3}{4}b - 2b - \frac{1}{3}b + \frac{5}{6}b + b$.

   Printed answer:

   • $-\frac{7}{12}b$.

   verified: the printed answer passed a computed check

   How it was checked

   • identity: passes -Rational(7,12)*b

5. Exercise 15, problem 13

   A lady bought a ribbon for $m$ cents, some tape for $d$ cents, and some thread for $c$ cents. She paid $x$ cents on the bill. How much remains due?

   Printed answer:

   • $m + d + c - x$ cts.

   unverified: no computed check settled this one (yet)

   How it was checked

   • other: not a kind the checker handles m + d + c - x

6. Exercise 15, problem 14

   A man travels $a$ miles north, then $x$ miles south, then 5 miles further south, and then $y$ miles north. How far is he from his starting point?

   Printed answer:

   • $a - x - 5 + y$ miles.

   unverified: no computed check settled this one (yet)

   How it was checked

   • other: not a kind the checker handles a - x - 5 + y

7. Exercise 15, problem 15

   $a + 2b + 3c$, $5a + 3b + c$, $c - a - b$.

   Printed answer:

   • $5a + 4b + 5c$.

   verified: the printed answer passed a computed check

   How it was checked

   • identity: passes 5*a + 4*b + 5*c

8. Exercise 15, problem 16

   $x + y - z$, $x - y - z$, $y - x + z$.

   Printed answer:

   • $x + y - z$.

   verified: the printed answer passed a computed check

   How it was checked

   • identity: passes x + y - z

9. Exercise 15, problem 17

   $x + 2y - 3z + a$, $2x - 3y + z - 4a$, $2a - 3x + y - z$.

   Printed answer:

   • $-3z - a$.

   verified: the printed answer passed a computed check

   How it was checked

   • identity: passes -3*z - a

10. Exercise 15, problem 18

    $x^3 + 3x^2 - x + 5$, $4x^2 - 5x^3 + 3 - 4x$, $3x + 6x^3 - 3x^2 + 9$.

    Printed answer:

    • $2x^3 + 4x^2 - 2x + 17$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes 2*x**3 + 4*x**2 - 2*x + 17

11. Exercise 15, problem 19

    $ca - bc + c^3$, $ab + b^3 - ca$, $a^3 - ab + bc$.

    Printed answer:

    • $a^3 + b^3 + c^3$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes a**3 + b**3 + c**3

12. Exercise 15, problem 2

    $5ab$, $6ab$, $ab$, $13ab$.

    Printed answer:

    • $25ab$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes 25*a*b

13. Exercise 15, problem 20

    $3a^m - a^{m-1} - 1$, $3a^{m-1} + 1 - 2a^m$, $a^{m-1} + 1$.

    Printed answer:

    • $2a^m + 1$.

    unverified: no computed check settled this one (yet)

    How it was checked

    • identity: the printed answer does not match the problem 2*a**m + 1

14. Exercise 15, problem 21

    $5a^5 - 16a^4b - 11a^2b^2c + 13ab$, $-2a^5 + 4a^4b + 12a^2b^2c - 10ab$, $6a^5 - a^4b - 6a^2b^2c + 10ab$, $-10a^5 + 8a^4b + a^2b^2c - 6ab$, $a^5 + 5a^4b + 6a^2b^2c - 7ab$.

    Printed answer:

    • $2a^2b^2c$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes 2*a**2*b**2*c

15. Exercise 15, problem 22

    $15x^3 + 35x^2 + 3x +7$, $7x^3 + 15x - 11x^2 + 9$, $9x - 10 + x^3 - 4x^2$.

    Printed answer:

    • $23x^3 - 20x^2 + 27x + 6$.

    unverified: no computed check settled this one (yet)

    How it was checked

    • identity: the printed answer does not match the problem 23*x**3 - 20*x**2 + 27*x + 6

16. Exercise 15, problem 23

    $9x^5y - 6x^4y^2 + x^3y^3 - 25xy^5$, $-22x^3y^3 - 3xy^5 - 9x^5y - 3x^4y^2$, $5x^3y^3 + x^5y + 21x^4y^2 + 20xy^5$.

    Printed answer:

    • $x^5y + 12x^4y^2 - 16x^3y^3 - 8xy^5$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes x**5*y + 12*x**4*y**2 - 16*x**3*y**3 - 8*x*y**5

17. Exercise 15, problem 24

    $x - y - z - a - b$, $x + y + z + a + b$, $x + y + z + a - b$, $x + y - z - a - b$, $x + y + z - a - b$.

    Printed answer:

    • $5x + 3y + z - a - 3b$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes 5*x + 3*y + z - a - 3*b

18. Exercise 15, problem 25

    $a^2c + b^2c + c^3 - abc - bc^2 - ac^2$, $a^2b + b^3 - bc^2 - ab^2 - b^2c - abc$, $a^3 + ab^2 + ac^2 - a^2b - abc - a^2c$.

    Printed answer:

    • $a^3 + b^3 + c^3 - 3abc$.

    unverified: no computed check settled this one (yet)

    How it was checked

    • identity: the printed answer does not match the problem a**3 + b**3 + c**3 - 3*a*b*c

19. Exercise 15, problem 26

    A regiment is drawn up in $m$ ranks of $b$ men each, and there are $c$ men over. How many men in the regiment?

    Printed answer:

    • $mb + c$ men.

    unverified: no computed check settled this one (yet)

    How it was checked

    • other: not a kind the checker handles m*b + c

20. Exercise 15, problem 27

    A man had $x$ cows and $z$ horses. After exchanging 10 cows with another man for 19 horses, what will represent the number that he has of each?

    Printed answer:

    • $x - 10$ cows; $z + 19$ horses.

    unverified: no computed check settled this one (yet)

    How it was checked

    • other: not a kind the checker handles x - 10; z + 19

21. Exercise 15, problem 28

    In a class of 52 pupils there are 8 more boys than girls. How many are there of each?

    Printed answer:

    • 22 girls; 30 boys.

    verified: the printed answer passed a computed check

    How it was checked

    • solve: passes, with the problem read into an equation {g: 22, b: 30}

22. Exercise 15, problem 3

    $-3ax^3$, $-5ax^3$, $-9ax^3$, $-ax^3$.

    Printed answer:

    • $-18ax^3$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes -18*a*x**3

23. Exercise 15, problem 4

    $-x$, $-5x$, $-11x$, $-25x$.

    Printed answer:

    • $-42x$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes -42*x

24. Exercise 15, problem 5

    $-2a^2$, $5a^2$, $3a^2$, $-7a^2$, $11a^2$.

    Printed answer:

    • $10a^2$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes 10*a**2

25. Exercise 15, problem 6

    $2abc^2$, $-5abc^2$, $abc^2$, $-8abc^2$.

    Printed answer:

    • $-10abc^2$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes -10*a*b*c**2

26. Exercise 15, problem 7

    $5x^2$, $3ab$, $-2ab$, $-4a^2$, $5ab$, $-2a^2$.

    Printed answer:

    • $6ab-x^2$.

    unverified: no computed check settled this one (yet)

    How it was checked

    • identity: the printed answer does not match the problem 6*a*b - x**2

27. Exercise 15, problem 8

    $5ax$, $-3bc$, $-2ax$, $7ax$, $bc$, $-2bc$.

    Printed answer:

    • $10ax - 4bc$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes 10*a*x - 4*b*c

28. Exercise 15, problem 9

    $4a^2 - 5a^2 - 8a^2 - 7a^2$.

    Printed answer:

    • $-16a^2$.

    verified: the printed answer passed a computed check

    How it was checked

    • identity: passes -16*a**2