Beginning Algebra, 11th Edition

SECTION 1.8 Simplifying Expressions^69

63.Concept Check Suppose that a student simplifies the expression as shown.

WHAT WENT WRONG?Work the problem correctly.

64.Explain how the procedure of changing to requires the use of the multiplicative iden-

tity element, 1.

Use the distributive property to rewrite each expression. Simplify if possible. See Example 9.

65. 
    
    
    
    66. 
        
        
        
        67. 
            
        
        
        
        
    
    
    
    


66. 
    
    
    
    69. 
        
        
        
        70. 
            
        
        
        
        
    
    
    
    


67. 
    
    
    
    72. 
        
        
        
        73. 
            
        
        
        
        
    
    
    
    

74. 75. 76.

77. 78. 79.

80. 81. 82.

83. 84. 85.

86. 87. 88.

Write each expression without parentheses. See Example 10.

89. 
    
    
    
    90. 
        
        
        
        91. 92.- 1 - 13 x- 15 y 2 93.- 1 - q+ 5 r- 8 s 2 94.- 1 - z+ 5 w- 9 y 2
        
        
        
        
    
    
    
    
    
    
    • 14 t+ 3 m 2 - 19 x+ 12 y 2 - 1 - 5 c- 4 d 2
    
    
    • 512 x- 5 y+ 6 z 2 5 x+ 15 9 p+ 18
    
    
    
    

813 r+ 4 s- 5 y 2 215 u- 3 v+ 7 w 2 - 318 x+ 3 y+ 4 z 2

4 s+ 4 r 712 v 2 + 715 r 2 1315 w 2 + 1314 p 2

• 8 z+ 8 w

2

5

• 110 b+ 20 a 2

4

3

112 y+ 15 z 2

• 
  
  
  
  • 51 y- 42 - 91 g- 42
  
  
  
  

1

3

19 x+ 52

-

1

4

• 81 r+ 32 - 111 x+ 42 18 x+ 32

51 w+ 42 71 z- 82 81 x- 62

519 + 82 6111 + 82 41 t+ 32

9

12

3

4

=- 30

=- 12 - 18

=- 3142 - 3162

- 314 - 62

- 314 - 62

OBJECTIVES

Simplifying Expressions

1.8

1 Simplify expressions.

2 Identify terms and
numerical
coefficients.

3 Identify like terms.

4 Combine like terms.

5 Simplify expressions
from word phrases.

OBJECTIVE 1 Simplify expressions. We use the properties of Section 1.7to do

this.

Simplifying Expressions

Simplify each expression.

(a) simplifies to

(b)

Distributive property

Associative property

= 12 m- 8 n Multiply.

= 14 # 32 m- 14 # 22 n

= 413 m 2 - 412 n 2

413 m- 2 n 2

4 x+ 8 + 9 4 x+ 17.

EXAMPLE 1

To simplify, we clear

the parentheses.