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 – 1Multiplicative property

EXAMPLE 2Distribute a negative number

Distribute – 1.

= – 2x + 11

(–1)(2x – 11)

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

GUIDED PRACTICE for Examples 1, 2 and 3

Use the distributive property to write an equivalent expression.

1. 2(x + 3) = 2x + 6

2. – (4 – y) = – 4 + y

3. (m – 5)(– 3m) = – 3m2 + 15m

4. (2n + 6) 12 = n + 3

GUIDED PRACTICE for Examples 1, 2 and 3

Identify the terms, like terms, coefficients, and constant terms of the expression – 7y + 8 – 6y – 13.

Coefficients: – 7, – 6

Like terms: – 7y and – 6y , 8 and – 13;

Constant terms: 8, – 13

Terms: – 7y, 8, – 6y, – 13

ANSWER

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 if you run

for 20 minutes.

SOLUTIONThe 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 and swim for 30 minutes.

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

6r + 450

GUIDED PRACTICE for Examples 4 and 5

6. Simplify the expression 5(6 + n) – 2(n – 2) = 34 + 3n.

7. WHAT IF? In Example 5, suppose your workout lasts 45 minutes. How many calories do you burn

if you run for 20 minutes? 30 minutes?

ANSWER

You burn 525 calories in your 45 minute workout if you run for 20 minutes.

You burn 585 calories in your 45 minute workout if you run for 30 minutes.