Copyright © 2013 Pearson Education, Inc. Section 1.8 Simplifying and Writing Algebraic Expressions.

Copyright © 2013 Pearson Education, Inc.

Section 1.8

Simplifying and Writing Algebraic

Expressions

Terms

A term is a number, a variable, or a product of numbers and variables raised to powers.

Examples of terms include4, z, 5x, and −6xy2.

The coefficient of a term is the number that appears in the term.

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Example

Determine whether each expression is a term. If it is a term, identify its coefficient.

a. 97 b. 17x c. 4a – 6b d. 9y2 Solutiona. A number is a term. The coefficient is 97.b. The product of a number and a variable is a term. The coefficient is 17.c. The difference of two terms in not a term.d. The product of a number and a variable with an exponent is a term. Its coefficient is 9.

Page 72

Example

Determine whether the terms are like or unlike.

a. 9x, −15x b. 16y2, 1 c. 5a3, 5b3 d. 11, −8z

Solutiona. The variable in both terms is x, with the same power of 1, so they are like terms.b. The term 1 has no variable and the 16 has a variable of y2. They are unlike terms.c. The variables are different, so they are unlike terms.d. The term 11 has no variable and the −8 has a variable of z. They are unlike terms.

Page 72

Example

Combine terms in each expression, if possible.

a. −2y + 7y b. 4x2 – 6x

Solutiona. Combine terms by applying the distributive property.

−2y + 7y = (−2 + 7)y = 5y

b. They are unlike terms, so they can not be combined.

Page 73

Example

Simplify each expression.

a. 13 + z – 9 + 7z b. 9x – 2(x – 5)Solutiona. 13 + z – 9 + 7z b. 9x – 2(x – 5)

= 13 +(– 9) + z + 7z

= 13 +(– 9) + (1+ 7)z

= 4 + 8z

= 9x + (– 2)x + (−2)(– 5)

= 9x – 2x + 10

= 7x + 10

Page 74

Example

Simplify each expression.

a. 6x2 – y + 9x2 – 3y b.

Solutiona.

18 6

3

a

6x2 – y + 9x2 – 3y

= 6x2 + 9x2 + (–1y) + (–3y)

= (6 + 9)x2 + (–1+ (– 3))y

= 15x2 –4y

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Optional step

Example

Simplify each expression.

a. 6x2 – y + 9x2 – 3y b.

Solutionb.

18 6

3

a

18 6

3

a

18 6

3 3

a

6 2a

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18 6

3

a

3

263 a

6 2a

Example

A sidewalk has a constant width w and comprises several short sections with lengths 11, 4, and 18 feet. a. Write and simplify an expression that gives the number of square feet of sidewalk. b. Find the area of the sidewalk if its width is 3 feet. Solutiona. 11w + 4w + 18w

= (11 + 4 + 18)w= 33w

b. 33w = 33 ∙ 3 = 99 square feet

11 ft

4 ft

18 ft

w

Page 76

End of chapter problems

• do 56, 58, 72 on page 77

• do 74, 76, 78 on page 77-78

• do 80, 82 on page 78

• do 84, 86, 88 on page 78

DONE

Objectives

• Terms

• Combining Like Terms

• Simplifying Expressions

• Writing Expressions