algebra 1 2.5 distributive property. vocabulary equivalent expressions: two expressions that have...
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Algebra 1 Algebra 1 2.5 Distributive Property
Vocabulary
Equivalent expressions: two expressions that have the same output value for every input value
Distributive Property: multiply the outside number to every number in the parenthesis
Term: the individual parts of an expression
Vocabulary
Coefficient: the number part of a term
Constant Term: a term that has a number part but no variable
Like Terms: terms that have the same variable part
Use the distributive property to write an equivalent expression.
EXAMPLE 1Apply the distributive property
1. 4(y + 3) =
2. (y + 7)y =
4. (2 – n)8 =
3. n(n – 9) =
4y + 12
y2 + 7y
n2 – 9n
16 – 8n
= – 15y + 3y2
2. (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
1. –2(x + 7)=– 2(x) + – 2(7)
5(–3y) – y(–3y)
Simplify.
= (– 1)(2x) – (–1)(11)
3. –(2x – 11) =of 21
Multiplicative 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.
SOLUTION
EXAMPLE 3 Identify parts of an expression
Terms: 3x, – 4, – 6x, 2
GUIDED PRACTICE
Use the distributive property to write an equivalent expression.
1. 2(x + 3) = 2x + 6
2. – (4 – y) = – 4 + y Distributive – 1
3. (m – 5)(– 3m) = m (– 3m) –5 (– 3m) Distributive – 3m
= – 3m2 + 15m Simplify.
4. (2n + 6) =12
122n + 61
2
= n + 3
12
Distribute
Simplify.
GUIDED PRACTICE
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;
SOLUTION
Terms: – 7y, 8, – 6y, – 13
Constant terms: 8, – 13
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
GUIDED PRACTICE
1. Simplify the expression 5(6 + n) – 2(n – 2).
5(6 + n) – 2(n – 2) = Distributive property
= 3n + 34 Combine like terms.
30 + 5n – 2n + 4
SOLUTION
Solve a multi-step problem
EXAMPLE 5
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 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 = 15 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
GUIDED PRACTICE
WHAT IF…
Suppose your workout lasts 45 minutes. How many calories do you run for 20 minutes? 30 minutes?
SOLUTION
The workout lasts 45 minutes, and your running time is r minutes. So, your swimming time is (45 – r) minutes.
GUIDED PRACTICE
STEP 1
C = 15 r + 9 (45 – r)
C = Write equation.
= 15r + 405 – 9r Distributive property
= 6r + 405 Combine like terms.
Write a verbal model. Then write an equation.
15 r + 9 (45 – r)
Amount burned
(calories)
Burning rate when running
(calories/minute)
Running time
(minutes)
Swimming time
(minutes)= +•
Burning rate when swimming (calories/minute) •
GUIDED PRACTICE
C = Write equation.
= 6(20) + 405 = 525 Substitute 20 for r. Then simplify.
STEP 2Find the value of C when r = 20.
6r + 405
Write equation.
= 6(30) + 405 = 585 Substitute 30 for r. Then simplify.
STEP 3Find the value of C when r = 30.
6r + 405C =
GUIDED PRACTICE
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.