ALGEBRAIC EXPRESSIONS

Excerpts

ALGEBRAIC EXPRESSIONS
An **algebraic expression** is any representation of a number by algebraic notation.
ALGEBRAIC EXPRESSIONS
A **term** is an algebraic expression not connected with any other by the sign plus or minus, or one of the parts of an algebraic expression with its own sign plus or minus. If no sign is written, the plus sign is understood.
ALGEBRAIC EXPRESSIONS
**Similar terms** are terms having the same letters affected by the same exponents. **Dissimilar terms** are terms which differ in letters or exponents, or both.
ALGEBRAIC EXPRESSIONS
A **monomial** is an algebraic expression of one term. A **polynomial** is an algebraic expression of more than one term. A polynomial of two terms is called a **binomial**, and one of three terms is called a **trinomial**.
ALGEBRAIC EXPRESSIONS
How do these terms compare with reference to degree? They are called *homogeneous* terms.
ALGEBRAIC EXPRESSIONS
Henry bought some apples at 3 cents apiece, and twice as many pears at 4 cents apiece, paying for the whole 66 cents. How many of each did he buy?
ALGEBRAIC EXPRESSIONS
The **degree of an algebraic expression** is the same as the degree of its highest term.

Equations

Problems

Exercise 14

Exercise 14, problem 1
Write a polynomial of five terms. Of what degree is it?
Printed answer:
- (none printed)
unverified: no computed check settled this one (yet)
How it was checked
- other: not a kind the checker handles
Exercise 14, problem 10
$2a + 3b + c$.
Printed answer:
- 11.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 11
On the STU-32 (STU, rpn):
```
2 ENTER 1 ×
```
```
3 ENTER 2 × +
```
```
3 +
```
Calculator: +11E+0; the book prints 11. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 11
$5b + 3a - 2c + 6x$.
Printed answer:
- 7.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 7
On the STU-32 (STU, rpn):
```
2 ENTER 5 ×
```
```
1 ENTER 3 ×
```
```
+
```
```
3 ENTER 2 ×
```
```
−
```
```
0 ENTER 6 ×
```
```
+
```
Calculator: +7000000000000000000000000000000000E-33; the book prints 7. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 12
$6bc - 3ax + 2xb - 5ac + 2cx$.
Printed answer:
- 21.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 21
On the STU-32 (STU, rpn):
```
6 ENTER 2 × 3 ×
```
```
3 ENTER 1 × 0 × −
```
```
2 ENTER 0 × 2 × +
```
```
5 ENTER 1 × 3 × −
```
```
2 ENTER 3 × 0 × +
```
Calculator: +2100000000000000000000000000000000E-32; the book prints 21. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 13
$3bcd + 5cxa - 7xab + abc$.
Printed answer:
- 78.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 78
On the STU-32 (STU, rpn):
```
3 ENTER 2 × 3 × 4 ×
```
```
5 ENTER 3 × 0 × 1 × +
```
```
7 ENTER 0 × 1 × 2 × −
```
```
1 ENTER 2 × 3 × +
```
Calculator: +7800000000000000000000000000000000E-32; the book prints 78. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 14
$2c^2 + 3b^3 + 4a^4$.
Printed answer:
- 46.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 46
On the STU-32 (STU, rpn):
```
2 ENTER 3 GOLD x² ×
```
```
2 ENTER 3 yˣ 3 × +
```
```
1 ENTER 4 yˣ 4 × +
```
Calculator: +46E+0; the book prints 46. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 15
$\frac{1}{2}a^3c - b^3 - c^3 - \frac{3}{4}abc^3$.
Printed answer:
- $-74$.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes -74
On the STU-32 (STU, rpn):
```
1 ENTER 2 ÷ 1 ENTER 3 yˣ × 3 ×
```
```
2 ENTER 3 yˣ −
```
```
3 ENTER 3 yˣ −
```
```
3 ENTER 4 ÷ 1 × 2 × 3 ENTER 3 yˣ × −
```
Calculator: -7400E-2; the book prints -74. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 16
$2a - b - \frac{2ab}{a + b}$.
Printed answer:
- $-1\frac{1}{3}$.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes -Rational(4, 3)
Exercise 14, problem 17
$2bc - \frac{3}{4}c^3 + 3ab - 2a - x + \frac{4}{15}bx$.
Printed answer:
- $-4\frac{1}{4}$.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes -Rational(17, 4)
Exercise 14, problem 18
$\frac{a^2bx + ab^2c + abc^2 + xac^2}{abc}$.
Printed answer:
- 5.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 5
On the STU-32 (STU, rpn):
```
1 GOLD x² 2 × 0 ×
```
```
1 ENTER 2 GOLD x² × 3 × +
```
```
1 ENTER 2 × 3 GOLD x² × +
```
```
0 ENTER 1 × 3 GOLD x² × +
```
```
1 ENTER 2 × 3 × ÷
```
Calculator: +500000000000000000000000000000000E-32; the book prints 5. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 19
Henry bought some apples at 3 cents apiece, and twice as many pears at 4 cents apiece, paying for the whole 66 cents. How many of each did he buy?
Printed answer:
- 6 apples; 12 pears.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {a: 6, p: 12}
Exercise 14, problem 2
Write a binomial of the fourth degree.
Printed answer:
- (none printed)
unverified: no computed check settled this one (yet)
How it was checked
- other: not a kind the checker handles
Exercise 14, problem 20
Sarah’s father told her that the difference between two-thirds and five-sixths of his age was 6 years. How old was he?
Printed answer:
- 36 years.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {A: 36}
On the STU-32 (STU, rpn):
```
5 ENTER 6 ÷
```
```
2 ENTER 3 ÷ −
```
```
6 x↔y ÷
```
Calculator: +3600000000000000000000000000000001E-32; the book prints 36. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 3
Write a polynomial with the terms of different degrees.
Printed answer:
- (none printed)
unverified: no computed check settled this one (yet)
How it was checked
- other: not a kind the checker handles
Exercise 14, problem 4
Write a homogeneous trinomial of the third degree.
Printed answer:
- (none printed)
unverified: no computed check settled this one (yet)
How it was checked
- other: not a kind the checker handles
Exercise 14, problem 5
Write two similar monomials of the fifth degree which shall differ as much as possible.
Printed answer:
- (none printed)
unverified: no computed check settled this one (yet)
How it was checked
- other: not a kind the checker handles
Exercise 14, problem 6
Write a homogeneous trinomial with one of its terms of the second degree.
Printed answer:
- (none printed)
unverified: no computed check settled this one (yet)
How it was checked
- other: not a kind the checker handles
Exercise 14, problem 7
Arrange according to the descending powers of $a$: $-80a^3b^3 + 60a^4b^2 + 108ab^5 + 48a^5b + 3a^6 - 27b^6 - 90a^2b^4$. What name? What degree?
Printed answer:
- (none printed)
unverified: no computed check settled this one (yet)
How it was checked
- other: not a kind the checker handles
Exercise 14, problem 8
Write a polynomial of the fifth degree containing six terms.
Printed answer:
- (none printed)
unverified: no computed check settled this one (yet)
How it was checked
- other: not a kind the checker handles
Exercise 14, problem 9
Arrange according to the ascending powers of $x$: 15x^2y^3 + 7x^5 - 3xy^5 - 60x^4y + y^7 + 21x^3y^2 What name? What degree? What is the degree of each term?
Printed answer:
- (none printed)
unverified: no computed check settled this one (yet)
How it was checked
- other: not a kind the checker handles