Basic Mathematics for College Students

Simplify by combining like terms.See Examples 7 and 8.

67. 
    
    
    
    68. 
        
    
    
    
    


68. 
    
    
    
    70. 
        
    
    
    
    


69. 
    
    
    
    72. 
        
    
    
    
    


70. 
    
    
    
    74. 
        
    
    
    
    


71. 
    
    
    
    76. 
        
    
    
    
    


72. 
    
    
    
    78. 
        
    
    
    
    


73. 
    
    
    
    80. 
        
    
    
    
    


74. 
    
    
    
    82. 
        
    
    
    
    


75. 
    
    
    
    84. 
        
    
    
    
    


76. 
    
    
    
    86. 
        
    
    
    
    

Simplify by combining like terms, if possible.See Example 9.

87. 
    
    
    
    88. 
        
    
    
    
    


88. 
    
    
    
    90. 
        
    
    
    
    


89. 6 m^2  6 m 6 92. 9 a^2  9 a 9


90. 
    
    
    
    94. 
        
    
    
    
    

Simplify.See Example 10.

95.

96.

97.

98.

99.

100. 
     

101. 
     

102. 
     

Simplify each expression.

103. 
     
     
     
     104. 
          
     
     
     
     


104. 
     
     
     
     106. 
          
     
     
     
     


105. 
     
     
     
     108. 
          
     
     
     
     


106. 
     
     
     
     110. 
          
     
     
     
     


107. 
     
     
     
     112. 
          
     
     
     
     


108. 5(1.2x) 114.5(6.4c)

72 a

7

8

ƒ

8

9

60 a b

3

20

r

4

15

b

aaa tttt

3

4



1

2

24 a g

5

6

rb

 4 r 7 r 2 rr v 3 v 6 v 2 v

6 4( 3 c7) 10 5( 5 g1)

TRY IT YOURSELF

40 a

3

8

y

1

4

b 40 a

4

5

b

36 a

2

9

x

3

4

b 36 a

1

2

b

6(3t6)3(11t3)

9(3r9)7(2r7)

4(d^2 3)(d^2 1)

2(s^2 7)(s^2 2)

12(m11) 11

2 z5(z3)

4 x^2  5 x 8 x 9 10 y^2  8 yy 7

3 x 4  5 x 1 4 b 9  9 b 9

15 y 10 y 20 y 9 z 7 z 19 z



5

18

x

7

18

 x

7

16

x

3

16

x

3

16

x

5

16

x

3

5

t

1

5

t

0.2r(0.6r) 1.1m(2.4m)

9.8c6.2c 5.7m4.3m

43 s^3  44 s^38 j^3  9 j^3

36 yy 9 y 32 aa 5 a

13 r 12 r 25 ss

 7 b^2  27 b^2  2 c^3  12 c^3

 4 x 4 x  16 y 16 y

3 x 7 x 12 y 15 y

115.

116.

117.

118.

In Exercises 119–122, recall that the perimeterof a figure is

equal to the sum of the lengths of its sides.

119. THE RED CROSS In 1891, Clara
     Barton founded the Red Cross. Its
     symbol is a white flag bearing a red
     cross. If each side of the cross has length
     x, write an expression that represents the
     perimeter of the cross.


120. BILLIARDS Billiard tables vary in size, but all
     tables are twice as long as they are wide.
     a. If the billiard table is feet wide, write an
     expression that represents its length.
     b. Write an expression
     that represents the
     perimeter of the
     table.

121. PING-PONG

Write an expression

that represents the

perimeter of the

Ping-Pong table.

122. SEWING Write
     an expression that
     represents the
     length of the yellow
     trim needed to
     outline a pennant
     with the given side
     lengths.


123. Explain why the distributive property applies to
     but not to.


124. Explain how to combine like terms. Give an example.

Evaluate each expression for , and.

125. 
     
     
     
     126. 
          
     
     
     
     

2 y 1

x

x

xy^2

2 y 1 x

x3, y 5 z 0

REVIEW

2(3x) 2(3x)

WRITING

(2x – 15) cm

(2x – 15) cm

x cm

x ft (x + 4) ft

x ft

x

x

APPLICATIONS

c^3  3 c^2  9 c 3 c^2  9 c 27

a^3  2 a^2  4 a 2 a^2  4 a 8

(z2)5(3z)

(c7)2(c3)

8.2 Simplifying Algebraic Expressions 657