the distributive property objective key vocabulary equivalent expressions distributive property
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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.