Basic Mathematics for College Students

7. a. Fill in the blanks to simplify the expression.

b. What property did you use in part a?

8. a. Fill in the blanks to simplify the expression.

b. What property did you use in part a?

9. Fill in the blanks.
   a.

b.

c.

d.

10. Fill in the blanks to combine like terms.
    a.

b.

c.

d. Like terms can be combined by adding or

subtracting the of the terms and

keeping the same with the same

exponents.

11. Simplify each expression, if possible.
    a. b.

c. d.

e. f.

12. Fill in the blanks: Distributing multiplication by
    changes the of each term within the parentheses.


13. Translate to symbols.
    a. Six times the quantity of minus four.

b. The opposite of the sum of and sixteen.

14. Write an equivalent expression for the given
    expression using fewer symbols.
    a. b. c.

d. 5 x(1) e. 16 t(6)

1 x  1 d 0 m

z

h

NOTATION

(x10) (x10)x 10

 1

2(3x)(3) 2  3 x 3

6( 7 x) 6  7 x

5(2x) 5  2 x

12  32 d 15  32 d

30 n^2  50 n^2 (  )n^2  n^2

4 m 6 m(  )m m

2(x4) 2 x 8

2(x4) 2 x 8

2(x4) 2 x 8

2(x4) 2 x 8

 6 y 2   y y

4(9t)(  )t t

CONCEPTS

Simplify.See Example 1.

15. 
    
    
    
    16. 
        
    
    
    
    


16. 
    
    
    
    18. 
        
    
    
    
    


17. 
    
    
    
    20. 
        
    
    
    
    


18. 
    
    
    
    22. 
        
    
    
    
    


19. 
    
    
    
    24. 
        
    
    
    
    


20. 
    
    
    
    26. 
        
    
    
    
    


21. 
    
    
    
    28. 
        
    
    
    
    


22. 
    
    
    
    30. 
        
    
    
    
    


23. 
    
    
    
    32. 
        
    
    
    
    


24. 
    
    
    
    34. 
        
    
    
    
    

Multiply.See Example 2.

35. 
    
    
    
    36. 
        
    
    
    
    


36. 
    
    
    
    38. 
        
    
    
    
    


37. 
    
    
    
    40. 
        
    
    
    
    


38. 
    
    
    
    42. 
        
    
    
    
    

Multiply.See Example 3.

43. 
    
    
    
    44. 
        
    
    
    
    


44. 
    
    
    
    46. 
        
    
    
    
    


45. 
    
    
    
    48. 
        
    
    
    
    


46. 
    
    
    
    50. 
        
    
    
    
    

Multiply.See Example 4.

51. 
    
    
    
    52. 
        
    
    
    
    


52. 
    
    
    
    54. 
        
    
    
    
    


53. 
    
    
    
    56. 
        
    
    
    
    


54. 
    
    
    
    58. 
        
    
    
    
    

Simplify.See Example 5.

59. 
    
    
    
    60. 
        
    
    
    
    


60. 
    
    
    
    62. 
        
    
    
    
    

Identify the like terms in each expression, if any.

See Example 6.

63.

64.

65.

66. 6 x^3  3 x^2  6 x

 12 m^4  3 m^3  2 m^2 m^3

3 y 4  11 y 6

3 x 2  2 x

(5.6y7) (4.8a3)

(x7) (y1)

25(2a 3 b1) 5(9s 12 t3)

4(7y4)2 8(2a3)4

(2y8)

1

2

(3w6)

2

3

(3t2)8 (2q1)9

1( 4 a1) 1( 2 x3)

15( 2 t6) 20( 4 z5)

6(13c3) 2(10s11)

6(6c7) 9(9d3)

0.4(x4) 2.2(2q1)

35 a

y

5



8

7

45 a b

x

5



2

9

b

3(4x9) 5(8x9)

5(x3) 4(x2)

27 a

2

3

8 a xb

3

4

yb

15 a

4

15

12 a wb

5

12

xb

9

7



7

9

k

5

3



3

5

g

4(6)( 4 m) 5(9)( 4 n)

5(4c)(3) 9(2h)(2)

(5.6x)(2) (4.4x)(3)

5 t 60 70 a 10

5( 7 q) 7(5t)

9(7m) 12 n(8)

3  4 t 9  3 s

GUIDED PRACTICE

656 Chapter 8 An Introduction to Algebra