2.5
Apply the Distributive Property
Goal
Your Notes
p Apply the distributive property.
VOCABULARY
Equivalent expressions
Distributive property
Terms
Coefficient
Constant term
Like terms
THE DISTRIBUTIVE PROPERTY
Let a, b, and c be real numbers.
42
Algebra
Numbers
a(b 1 c) 5 ab 1
4(2 1 3) 5
1
(b 1 c)a 5 ba 1
(3 1 5)2 5
1
a(b 2 c) 5 ab 2
7(5 2 3) 5
2
(b 2 c)a 5 ba 2
(6 2 4)9 5
2
Lesson 2.5 • Algebra 1 Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
Your Notes
Be sure to
distribute the
factor outside of
the parentheses
to all of the
numbers inside the
parentheses.
Apply the distributive property
Example 1
Use the distributive property to write an equivalent
equation.
Solution
a. 4(a 1 3) 5
b. (a 1 5)6 5
c. 3(x 2 8) 5
d. (4 2 x)(x) 5
Distribute a negative number
Example 2
Use the distributive
property to combine
like terms with
variable parts.
Your expression is
simplified if there
are no grouping
symbols and all
like terms are
combined.
Use the distributive property to write an equivalent
equation.
Solution
a. 23(7 1 x)
5
(7) 1
Distribute
(x)
.
.
5
b. (6 2 a)(22a)
5 6(
) 2 a(
)
Distribute
.
.
5
Checkpoint Use the distributive property to write an
equivalent equation.
1. 5(n 1 4)
2. 2a(3 1 a)
Example 3
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Lesson 2.5 • Algebra 1 Notetaking Guide
43
Your Notes
Example 3
Identify parts of an expression
Identify the terms, like terms, coefficients, and constant
terms of the expression 2x 2 5 1 8x 2 3.
Solution
Write the expression as a
sum.
Terms:
Like terms:
Coefficients:
Constant terms:
Checkpoint Identify the terms, like terms, coefficients,
and constant terms of the expressions.
3. 10 1 3a 2 4 2 6a
4. 7y 2 11 2 4y 2 1
Homework
44
Lesson 2.5 • Algebra 1 Notetaking Guide
Copyright © Holt McDougal. All rights reserved.