1. EXAMPLE 1
Apply the distributive property
Use the distributive property to write an equivalent expression.
a. 4(y + 3) =
4y + 12
b. (y + 7)y =
y2 + 7y
c. n(n – 9) =
n2 – 9n
d. (2 – n)8 =
16 – 8n

2. Distribute a negative number
EXAMPLE 2
Distribute a negative number
Use the distributive property to write an equivalent
expression.
a. –2(x + 7)=
– 2(x) + – 2(7)
Distribute – 2.
= – 2x – 14
Simplify.
b. (5 – y)(–3y) =
5(–3y) – y(–3y)
Distribute – 3y.
= – 15y + 3y2
Simplify.

3. Distribute a negative number
EXAMPLE 2
Distribute a negative number
c. –(2x – 11) =
(–1)(2x – 11)
of – 1
Multiplicative property
= (– 1)(2x) – (–1)(11)
Distribute – 1.
= – 2x + 11
Simplify.

4. EXAMPLE 3
Identify parts of an expression
Identify the terms, like terms, coefficients, and constant terms of the expression 3x – 4 – 6x + 2.
SOLUTION
Write the expression as a sum: 3x + (–4) + (–6x) + 2
Terms: 3x, – 4, – 6x, 2
Like terms: 3x and – 6x; – 4 and 2
Coefficients: 3, – 6
Constant terms: – 4, 2

5. GUIDED PRACTICE
for Examples 1, 2 and 3
Use the distributive property to write an equivalent expression.
(x + 3) =
2x + 6
2. – (4 – y) =
– 4 + y
3. (m – 5)(– 3m)
= – 3m2 + 15m
4. (2n + 6) 1 2
= n + 3

6. GUIDED PRACTICE
for Examples 1, 2 and 3
Identify the terms, like terms, coefficients, and constant terms of the expression – 7y + 8 – 6y – 13.
Terms: – 7y, 8, – 6y, – 13
ANSWER
Like terms: – 7y and – 6y , 8 and – 13;
Coefficients: – 7, – 6
Constant terms: 8, – 13

7. Standardized Test Practice
EXAMPLE 4
Standardized Test Practice
Simplify the expression 4(n + 9) – 3(2 + n). A B C D
n + 3
5n + 30
n + 30
5n + 3
4(n + 9) – 3(2 + n) =
4n + 36 – 6 – 3n
Distributive property
= n + 30
Combine like terms.
ANSWER
The correct answer is B. D C B A

8. Solve a multi-step problem
EXAMPLE 5
Solve a multi-step problem
EXERCISING
Your 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.
SOLUTION
The workout lasts 50 minutes, and your running time is r minutes. So, your swimming time is (50 – r) minutes.

9. Solve a multi-step problem
EXAMPLE 5
Solve a multi-step problem
STEP 1
Write a verbal model. Then write an equation.
Amount burned (calories)
Burning rate when running (calories/minute)
Running time (minutes)
Swimming time (minutes) = + •
Burning rate when swimming (calories/minute)
C = r (50 – r)
C =
15r + 9(50 – r)
Write equation.
= 15r – 9r
Distributive property
= 6r + 450
Combine like terms.

10. Solve a multi-step problem
EXAMPLE 5
Solve a multi-step problem
STEP 2
Find the value of C when r = 20.
C =
6r + 450
Write equation.
= 6(20) = 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.

11. 6. Simplify the expression 5(6 + n) – 2(n – 2)
GUIDED PRACTICE
for Examples 4 and 5
6. Simplify the expression 5(6 + n) – 2(n – 2)
= n.
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.