=
5(
x
−
3)
Distributive Property
The factor 5 represents the number of books purchased. The factor
(
x
−
3) represents the price of each book. This factor is a difference of
two terms, showing that the price
x
of each book is decreased by $3.
So, the factored expression shows a $3 discount for every book
you buy. The original expression shows a total savings of $15.
EXAMPLE
Factoring an Algebraic Expression
3
Factor the expression using the GCF.
1.
7
+
14
2.
44
−
11
3.
18
−
12
4.
70
+
95
5.
60
−
36
6.
100
−
80
7.
84
+
28
8.
48
+
80
9.
2
x
+
10
10.
15
x
+
6
11.
26
x
−
13
12.
50
x
−
60
13.
36
x
+
9
14.
14
x
−
98
15.
10
x
−
25
y
16.
24
y
+
88
x
17.
REASONING
The whole numbers
a
and
b
are divisible by
c
. Is
a
+
b
divisible by
c
?
Is
b
−
a
divisible by
c
? Explain your reasoning.
18.
OPEN-ENDED
Write five expressions that are equivalent to 8
x
+
16.
19.
GEOMETRY
The area of the parallelogram is
4 ft
(4
x
+
16) square feet. Write an expression
for the base.
20.
STRUCTURE
You buy 37 concert tickets for $8 each, and then sell all 37 tickets for
$11 each. The work below shows two ways you can determine your profit. Describe
each solution method. Which do you prefer? Explain your reasoning.
profit
=
37(11)
−
(37)8
=
407
−
296
=
$111
profit
=
37(11)
−
(37)8
=
37(11
−
8)
=
37(3)
=
$111

Quiz
3.3–3.4
142
Chapter 3
Algebraic Expressions and Properties
Tell which property the statement illustrates.
(Section 3.3)
1.
3.5
⋅
z
=
z
⋅
3.5
2.
14
+
(35
+
w
)
=
(14
+
35)
+
w
Simplify the expression. Explain each step.
(Section 3.3)
3.
3.2
+
(
b
+
5.7)
4.
6
⋅
(10
⋅
k
)
Use the Distributive Property and mental math to find the
product.
(Section 3.4)
5.
6
×
49
6.
7
×
86
Use the Distributive Property to simplify the expression.
(Section 3.4)
7.
5(
x
−
8)
8.
7(
y
+
3)
Simplify the expression.
(Section 3.4)
9.
6
q
+
2
+
3
q
+
5
10.
4
r
+
3(
r
−
2)
Factor the expression using the GCF.
(Section 3.4)
11.
12
+
21
12.
16
x
−
36
13.
GEOMETRY
The expression 18
+
7
+
(18
+
2
x
)
+
7 represents
the perimeter of the trapezoid. Simplify the expression.
(Section 3.3)
14.
MOVIES
You and four of your friends go to a
movie and each buy popcorn.
(Section 3.4)
a.
Use the Distributive Property to write an expression for the total cost
to buy movie tickets and popcorn. Simplify the expression.
b.
Choose a reasonable value for
x.
Evaluate the expression.
15.
GEOMETRY
The length of a rectangle is
16 inches, and its area is (32
x
+
48) square inches.
Factor the expression for the area. Write an
expression for the width.
(Section 3.4)
Progress Check
18
à
2
x
18
7
7
Movie Tickets
Snacks
Student $8
Adult $10
Candy $3
Popcorn $
x

Chapter Review
143
3.2
Writing Expressions
(pp. 118–123)
Write the phrase as an expression.
a.
a number
z
decreased by 18
z
−
18
The phrase
decreased by
means
subtraction
.
b.
the sum of 7 and the product of a number
x
and 12
7
+
12
x
The phrase
sum of
means
addition
.
The phrase
product of
means
multiplication
.
3
Chapter Review
Review Key Vocabulary
Review Examples and Exercises
algebraic expression,
p. 112
terms,
p. 112
variable,
p. 112
coefficient,
p. 112
constant,
p. 112
equivalent expressions,
p. 128
like terms,
p. 136
factoring an expression,
p. 140
Vocabulary Help
a. Evaluate
a
÷
b
when
a
=
48 and
b
=
8.

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