Intermediate Algebra (11th edition)

300 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions

63.Concept Check Use the special product rule to find the

product.

64.Concept Check Repeat Exercise 63for the product

In Exercises 65 –74, the factors involve fractions or decimals. Apply the methods of this sec-

tion, and find each product.

65. 
    
    
    
    66. 
        
    
    
    
    


66. 
    
    
    
    68. 
        
    
    
    
    

69. 70.

71. 72.

73. 74.

Find each product. See Example 7.

75. 
    
    
    
    76. 
        
    
    
    
    


76. 
    
    
    
    78. 
        
    
    
    
    


77. 
    
    
    
    80. 
        
    
    
    
    


78. 
    
    
    
    82. 
        
    
    
    
    


79. 
    
    
    
    84. 
        
        
        
        85. 
            
        
        
        
        
    
    
    
    


80. 
    
    
    
    87. 
        
        
        
        88. 
            
        
        
        
        
    
    
    
    

Brain Busters Find each product.

89. 
    
    
    
    90. 
        
    
    
    
    


90. 
    
    
    
    92. 
        
    
    
    
    


91. 
    
    
    
    94. 
        
    
    
    
    


92. 
    
    
    
    96. 
        
    
    
    
    

In Exercises 97–100, two expressions are given. Replace x with 3 and y with 4 to show that, in

general, the two expressions are not equivalent.

97. ; 98. ;


98. ; 100. ;

Find the area of each figure. Express it as a polynomial in descending powers of the vari-

able x. Refer to the formulas on the inside covers of this book if necessary.

101. 
     
     
     
     102. 
          
     
     
     
     

103. 104.

1 x+y 24 x^4 +y^41 x+y 25 x^5 +y^5

1 x+y 22 x^2 +y^21 x+y 23 x^3 +y^3

ab 1 a+b 21 a+ 2 b 21 a- 3 b 2 mp 1 m-p 21 m- 2 p 212 m+p 2

1 m^2 - 2 mp+p^221 m^2 + 2 mp-p^2213 +x+y 21 - 3 +x-y 2

14 z-x 21 z^3 - 4 z^2 x+ 2 zx^2 - x^3213 r+ 2 s 21 r^3 + 2 r^2 s-rs^2 + 2 s^32

12 a+b 213 a^2 + 2 ab+b^221 m- 5 p 21 m^2 - 2 mp+ 3 p^22

1 x+ 3 y 23 1 q- 224 1 r+ 324

1 y+ 223 1 z- 323 15 r-s 23

312 h-k 2 +j 4312 h-k 2 - j 4 313 m-y 2 +z 4313 m-y 2 - z 4

312 a+b 2 - 34312 a+b 2 + 34 31 m+p 2 - 5431 m+p 2 + 54

312 a+b 2 - 342 314 k+h 2 - 442

315 x+ 12 + 6 y 42 313 m- 22 +p 42

1 0.2 x-1.4y 22 1 0.3x-1.6y 22

aq-

3

4

rb

2

ak-

5

7

pb

2

a 3 t-

5

4

ba 3 t+

5

4

a 4 x- b

2

3

ba 4 x+

2

3

b

a 5 r+

2

3

a 3 w+ yb1r- 5 y 2

1

4

zb1w- 2 z 2

1 0.2 x+1.3 21 0.5x-0.1 2 1 0.1y+2.1 21 0.5y-0.4 2

202 #198.

101 # 99

1 x+y 21 x-y 2 =x^2 - y^2

3 x – 2y

3 x + 2y

x^2 + 8

x^2 + 8

5 x + 6

3 x – 4

x^2 + 2x + 4

2 x + 3