Chapter 8: Equations & Chapter 8: Equations & InequalitiesInequalities

8.1 – Simplifying Algebraic 8.1 – Simplifying Algebraic ExpressionsExpressions

Simplify Expressions

Simplify 3(x + 5).

3(x + 5) = 3(x) + 3(5)

= 3x + 15

Distributive Property

Simplify.

“SIMPLIFY”

-Eliminate parentheses

-Combine all like terms

“SIMPLIFY”

-Eliminate parentheses

-Combine all like terms

A. A

B. B

C. C

D. D

A. x + 8

B. x + 12

C. 2x + 6

D. 2x + 12

Simplify 2(x + 6).

Simplify (a + 4)7.

(a + 4)7 = a ● 7 + 4 ● 7

= 7a + 28

Distributive Property

Simplify.

1. A

2. B

3. C

4. D

A. 3a + 27

B. 3a + 18

C. 3a + 9

D. a + 18

Simplify (a + 6)3.

Simplify Expressions (Subtraction)

Simplify (q – 3)9.

(q – 3)9 Distributive Property

Simplify

= (q)9

= 9q – 27

– (3)9

1. A

2. B

3. C

4. D

A. q – 16

B. q – 10

C. 8q – 16

D. 8q – 10

Simplify (q – 2)8.

Simplify –3(z – 7).

Distributive Property

Simplify.

–3(z –7) = –3(z)

= –3z + 21

+ (–3)(–7)

REMEMBER: (-) x (-) = (+)

1. A

2. B

3. C

4. D

A. –2z + 8

B. –2z – 8

C. –2z – 4

D. –2z

Use the Distributive Property to rewrite –2(z – 4).

Identify the terms, like terms, coefficients, and constants in 3x – 5 + 2x – x + 7.

Terms:

Like Terms:

Coefficients:

Constants:

3x, -5, 2x, -x, 7

3x, 2x, -x

3, 2, -1

-5, 7

-5, 7

Simplify 8z + 2z – 5 – 9z + 2.

8z + 2z – 5 – 9z + 2

Locate like terms.

= 8z + 2z – 9z – 5 + 2Commutative Property.

= 1z – 3 Simplify

(combine like terms) = z – 3

1. A

2. B

3. C

4. D

A. –z

B. –z + 2

C. z –1

D. –2z

Simplify 6z + z – 2 – 8z + 2.

ANSWERS TO

1)D

2)B

3)C

4)A

5)A

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