Beginning Algebra, 11th Edition

Complete solution available
on the Video Resources on DVD

5.6 EXERCISES

1.Concept Check Consider the square.

(a)What is the simplest form of the square of the first term,?

(b)What is the simplest form of twice the product of the two terms,?

(c)What is the simplest form of the square of the last term,?

(d)Write the final product, which is a trinomial, using your results in parts (a)– (c).

2.Explain in your own words how to square a binomial. Give an example.

Find each product. See Examples 1 and 2.

3. 
   
   
   
   4. 
      
      
      
      5. 
         
      
      
      
      
   
   
   
   


4. 
   
   
   
   7. 
      
      
      
      8. 
         
      
      
      
      
   
   
   
   


5. 
   
   
   
   10. 
       
       
       
       11. 
           
       
       
       
       
   
   
   
   


6. 
   
   
   
   13. 
       
       
       
       14. 
           
       
       
       
       
   
   
   
   


7. 
   
   
   
   16. 
       
       
       
       17. 
           
       
       
       
       
   
   
   
   


8. 
   
   
   
   19. 
       
       
       
       20. 21.Concept Check Consider the product.
           (a)What is the simplest form of the product of the first terms,?
           (b)Multiply the outer terms,. Then multiply the inner terms,. Add the
           results. What is this sum?
           (c) What is the simplest form of the product of the last terms,?
           (d)Write the final product, using your results in parts (a) and (c). Why is the sum found
           in part (b) omitted here?
           22.Explain in your own words how to find the product of the sum and the difference of two
           terms. Give an example.
       
       
       
       
   
   
   
   

Find each product. See Examples 3 and 4.

23. 
    
    
    
    24. 
        
        
        
        25. 
            
        
        
        
        
    
    
    
    


24. 
    
    
    
    27. 
        
        
        
        28. 
            
        
        
        
        
    
    
    
    


25. 
    
    
    
    30. 
        
        
        
        31. 
            
        
        
        
        
    
    
    
    


26. 
    
    
    
    33. 
        
        
        
        34. 
            
        
        
        
        
    
    
    
    


27. 
    
    
    
    36. 
        
        
        
        37. 
            
        
        
        
        
    
    
    
    

38. 39. 40.

41.Does equal in general? Explain.

42.Does equal in general? Explain.

Find each product. See Example 5.

43. 
    
    
    
    44. 
        
        
        
        45. 
            
            
            
            46. 
                
            
            
            
            
        
        
        
        
    
    
    
    


44. 
    
    
    
    48. 
        
        
        
        49. 
            
            
            
            50. 
                
            
            
            
            
        
        
        
        
    
    
    
    


45. 
    
    
    
    52. 
        
        
        
        53. 
            
            
            
            54. 
                
            
            
            
            
        
        
        
        
    
    
    
    


46. 
    
    
    
    56. 
        
        
        
        57. 58.- 5 r 1 r+ 123 59. 1 x+y 221 x-y 22 60. 1 s+ 2221 s- 222
        
        
        
        
    
    
    
    

2 x 1 x+ 123 3 y 1 y+ 223 - 4 t 1 t+ 323

14 x- 124 12 x- 124 13 r- 2 t 24 12 z+ 5 y 24

1 r+ 523 1 p+ 323 12 a+ 123 13 m+ 123

1 x+ 123 1 y+ 223 1 t- 323 1 m- 523

1 a+b 23 a^3 +b^3

1 a+b 22 a^2 +b^2

a 7 x+ q 15 q- 1215 q+ 12 p 13 p+ 7213 p- 72

3

7

ba 7 x-

3

7

b

a 9 y+

2

3

ba 9 y-

2

3

a b

2

3

+rba

2

3

a -rb

3

4

• xba

3

4

+xb

113 r+ 2 z 2113 r- 2 z 2 12 x^2 - 5212 x^2 + 52 19 y^2 - 2219 y^2 + 22

15 y+ 3 x 215 y- 3 x 2 13 x+ 4 y 213 x- 4 y 2 110 x+ 3 y 2110 x- 3 y 2

17 - 2 x 217 + 2 x 2 15 x+ 2215 x- 22 12 m+ 5212 m- 52

1 k+ 521 k- 52 1 a+ 821 a- 82 14 - 3 t 214 + 3 t 2

3 y 1 - 3 y 2

7 x 1 - 3 y 2 3 y 17 x 2

7 x 17 x 2

17 x+ 3 y 217 x- 3 y 2

2 x 17 x- 222 - 14 r- 222 - 13 y- 822

t 13 t- 122 x 12 x+ 522 3 t 14 t+ 122

a 5 x+

2

5

yb

2

a 6 m-

4

5

nb

2

19 y+ 4 z 22

15 p+ 2 q 22 18 a+ 3 b 22 14 a+ 5 b 22

1 z- 522 1 x+ 2 y 22 1 p- 3 m 22

1 m+ 222 1 x+ 822 1 r- 322

32

214 x 2132

14 x 22

14 x+ 322

338 CHAPTER 5 Exponents and Polynomials

http://www.ebook777.com

http://www.ebook777.com