© Imagine Learning 1
Name: _______________________________________________________________________ Date: ____________________________________
How can I use the distributive property to write
equivalent expressions?
Review
Equivalent Expressions and the Distributive Property
The distributive property states that the product of a factor times a sum is equal to the sum
of the products of that factor times each addend.
a (b + c) = ab + ac
Write an expression equivalent to 3(x + 6).
To “distribute” the 3 to each addend
in parentheses, multiply each
addend by 3.
3(x + 6) = 3(x) + 3(6)
3(x + 6) = 3x + 18
Write an expression equivalent to 2f + 8.
The greatest common factor (GCF) of 2f
and 8 is 2. Write each term as a product
of 2 and another value.
2f + 8 = 2( f ) + 2(4)
2f + 8 = 2( f + 4)
Use the distributive property to write an equivalent expression. The rst two have been
started for you.
1.
1
2
(4x + 8) =
1
2
(4x) +
1
2
( 8 )
1
2
(4x + 8) = 2x + 4
2. 5g + 25
The GCF of 5g and 25 is 5 .
5g + 25 = 5( g + 5 )
3. 10(3a + 2b)
10( 3a ) + 10( 2b ) = 30a + 20b
4. 7(p + 11) = 7p + 77
5. 9 + 81y = 9(1 + 9y)
Practice
© Imagine Learning 2
Name: _______________________________________________________________________ Date: ____________________________________
Review
Equivalent Expressions and the Distributive Property
How does the distributive property allow you to create equivalent
expressions?
The distributive property allows you to distribute multiplication and to rewrite an expression without parentheses.
You can use substitution to determine if two expressions are equivalent.
Determine if each pair of expressions is equivalent.
6(x + 2) and 6x + 12
Step 1: Let x = 1.
Step 2: 6(1 + 2) 6(1) + 12
6(3) 6 + 12
18 18
Step 3: When x = 1, the
value of each
expression is 18.
The expressions
are equivalent.
5y + 10 and 2(y + 12)
Step 1: Let y = 2.
Step 2: 5(2) + 10 2(2 + 12)
10 + 10 2(14)
20 28
Step 3: When y = 2, the
expressions have
dierentvalues.
The expressions
are not equivalent.
Determine if expressions
are equivalent
1. Substitute the same
value for the variables.
2. Evaluate each
expression.
3. Compare the values.
Determine if the expressions are equivalent. Circle Yes or No. The rst one has been started
for you.
1. Is 7p + 28 equivalent to 7(p + 4)? Yes / No
Let p = 3.
7(3) + 28 = 21 + 28 = 49 7(3 + 4) = 7(7) = 49
2. Is 2x + 1 equivalent to 2(x + 0.5)? Yes / No
Let x = 2.
2( 2 ) + 1 = 4 + 1 = 5 2( 2 + 0.5) = 2( 2.5 ) = 5
3. Is 3t + 3 equivalent to 9(t + 1)? Yes / No
Let t = 5.
3(5) + 3 = 15 + 3 = 18 9(5 + 1) = 9(6) = 54
4. Is 1.5a + 7.5 equivalent to 2(a + 4.5)? Yes / No
Let a = Answers will vary. Sample work is shown.
Let a = 1.
1.5(1) + 7.5 = 1.5 + 7.5 = 9 2(1 + 4.5) = 2(5.5) = 11
Practice