The Distributive PropertyObjective

Key Vocabulary• equivalent expressions• distributive property

Use the distributive property to write an equivalent expression.

EXAMPLE 1Apply the distributive property

a. 4(y + 3) =

b. (y + 7)y =

d. (2 – n)8 =

c. n(n – 9) =

4y + 12

y2 + 7y

n2 – 9n

16 – 8n

= – 15y + 3y2

b. (5 – y)(–3y) =

Simplify.

Simplify.

Distribute – 3y.

= – 2x – 14

Distribute – 2.

Use the distributive property to write an equivalent expression.

EXAMPLE 2Distribute a negative number

a. –2(x + 7)= – 2(x) + – 2(7)

5(–3y) – y(–3y)

Simplify.

= (– 1)(2x) – (–1)(11)

c. –(2x – 11) =of 21

Multiplicative property

EXAMPLE 2Distribute a negative number

Distribute – 1.

= – 2x + 11

(–1)(2x – 11)

Terms and Coefficients

Identify parts of an expression

Constant terms: – 4, 2

Coefficients: 3, – 6

Like terms: 3x and – 6x; – 4 and 2

Identify the terms, like terms, coefficients, and constant terms of the expression 3x – 4 – 6x + 2.

Write the expression as a sum: 3x + (–4) + (–6x) + 2

SOLUTION

EXAMPLE 3 Identify parts of an expression

Terms: 3x, – 4, – 6x, 2

Standardized Test PracticeEXAMPLE 4

ANSWER

The correct answer is B. DCBA

Simplify the expression 4(n + 9) – 3(2 + n).

4(n + 9) – 3(2 + n) = Distributive property

= n + 30 Combine like terms.

A B C D n + 35n + 30 n + 30 5n + 3

4n + 36 – 6 – 3n

Solve a multi-step problem

EXAMPLE 5

EXERCISINGYour daily workout plan involves a total of 50 minutes of running and swimming. You burn 15 calories per minute when running and 9 calories per minute when swimming. Let r be the number of minutes that you run. Find the number of calories you burn in your 50 minute workout if you run for 20 minutes.

SOLUTION

The workout lasts 50 minutes, and your running time is r minutes. So, your swimming time is (50 – r) minutes.

Solve a multi-step problem

EXAMPLE 5

STEP 1

C = Write equation.

= 15r + 450 – 9r Distributive property

= 6r + 450 Combine like terms.

Write a verbal model. Then write an equation.

15r + 9(50 – r) C = 5 r + 9 (50 – r)

Amount burned

(calories)

Burning rate when running

(calories/minute)

Running time

(minutes)

Swimming time

(minutes)= +•

Burning rate when swimming (calories/minute)

•

Solve a multi-step problemEXAMPLE 5

C = Write equation.

= 6(20) + 450 = 570 Substitute 20 for r. Then simplify.

ANSWER

You burn 570 calories in your 50 minute workout if you run for 20 minutes.

STEP 2Find the value of C when r = 20.

6r + 450

Classwork

Complete the following problems.