ALGEBRA READINESSChapter 5 Section 6

5.6: Use the Distributive Property• The parts of an expression that are added together are the

terms of the expression. • A term that has no variable part is a constant term. • The number part of a variable part is called the coefficient of

the term.• Like terms have the same variable raised to the same power.• You can combine like terms by adding the coefficients of the

terms.

Distributive Property

The product of a number and the sum (or difference) of two other numbers is equal to the sum (or difference) of the products of the number and each other.

a(b + c) = ab + ac a(b – c) = ab – ac

Example 1 Identifying the Properties of Multiplication

Identify the property illustrated.

Commutative property of multiplicationa.

3

1x •

3

1• x=

Statement Property Illustrated

b.6

5– ( )1–•

6

5= Multiplicative property of – 1

c. 2.73–( )• x • = 3– • x( )• 2.7Associative property of multiplication

Multiplicative property of zerod.7

3– 0• = 0

Example 1 Identifying the Properties of Multiplication

Identify the property illustrated.

Statement Property Illustrated

Inverse property of multiplicatione.

8

18 • = 1

Identity property of multiplicationf. 9.8 • 1 = 9.8

Identify the property illustrated.

1. x– • 1 = x–

ANSWER Identity property

2.3

2

7

5– •

8

3• =

7

5– •

8

3

3

2•

ANSWER Associative property

3. • =0 ( )21.5– 0

ANSWER Property of zero

Practice for Example 1

Example 2 Using the Distributive Property

a. ( )5x –3.2– = ( )x3.2– – 3.2–( )( )5 Distributive property

= 3.2x– – 16–( ) Multiply.

= 3.2x– 16+ Subtraction rule

b.4

3– x –

2

7 y4 =2

74– ( )x4 – y

4

34 Distributive property

Multiply.– 14y= 4x3 –

Use the distributive property to write an equivalent expression.

3. ( )2.4+x3–

4. ( )12y16x– ––4

3

5. ( )2.28.7m –6

6. w –2

192

ANSWER 9y12x +

ANSWER 13.252.2m –

ANSWER 192w –

ANSWER 7.23x ––

Practice for Example 2

Use the distributive property to write an equivalent expression.

7. ( )y70.8– –

8. ( )2+3z0.5–

ANSWER 0.8y5.6 +–

ANSWER 11.5z– –

Practice for Example 2

Example 3 Combining Like Terms

a. 5x7x + x= ( )5+7 Distributive property

= 12x Add.

b. 8y6y + 9+– y= ( )8+6 9+– Distributive property

= 2y 9+ Add.

Example 4 Simplifying Expressions

3( )x7 – 4x+ Distributive property= 21 – 3x 4x+

Subtraction rule= 21 4x++ ( )3x–

x= ( )4+3– Distributive property21 +

Simplify.= 21 + x

Simplify the expression by combining like terms.

ANSWER21r

10. w1.7w – 3.2w 12.9w– – ANSWER 15.4w–

43

–41

r r+ r9.

Practice for Examples 3 and 4

Simplify the expression.

11. ( )2+8x5– 3– ANSWER 40x– – 13

ANSWER 3r – 512. ( )104r21

r + –

Practice for Examples 3 and 4