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Mathematics LibreTexts

1.9.1: Review Exercises

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Review Exercises

Real Numbers: Algebra Essentials

For the following exercises, perform the given operations.

1.

( 532 ) 2 6 ( 532 ) 2 6

2.

64÷( 28 )+14÷7 64÷( 28 )+14÷7

3.

2 5 2 +6÷2 2 5 2 +6÷2

For the following exercises, solve the equation.

4.

5x+9=−11 5x+9=−11

5.

2y+ 4 2 =64 2y+ 4 2 =64

For the following exercises, simplify the expression.

6.

9( y+2 )÷32+1 9( y+2 )÷32+1

7.

3m( 4+7 )m 3m( 4+7 )m

For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer.

8.

11

9.

0

10.

5 6 5 6

11.

11 11

Exponents and Scientific Notation

For the following exercises, simplify the expression.

12.

2 2 2 4 2 2 2 4

13.

4 5 4 3 4 5 4 3

14.

( a 2 b 3 ) 4 ( a 2 b 3 ) 4

15.

6 a 2 a 0 2 a −4 6 a 2 a 0 2 a −4

16.

( xy ) 4 y 3 2 x 5 ( xy ) 4 y 3 2 x 5

17.

4 −2 x 3 y −3 2 x 0 4 −2 x 3 y −3 2 x 0

18.

( 2 x 2 y ) −2 ( 2 x 2 y ) −2

19.

( 16 a 3 b 2 ) ( 4a b −1 ) −2 ( 16 a 3 b 2 ) ( 4a b −1 ) −2

20.

Write the number in standard notation: 2.1314× 10 −6 2.1314× 10 −6

21.

Write the number in scientific notation: 16,340,000

Radicals and Rational Expressions

For the following exercises, find the principal square root.

22.

121 121

23.

196 196

24.

361 361

25.

75 75

26.

162 162

27.

32 25 32 25

28.

80 81 80 81

29.

49 1250 49 1250

30.

2 4+ 2 2 4+ 2

31.

4 3 +6 3 4 3 +6 3

32.

12 5 13 5 12 5 13 5

33.

−243 5 −243 5

34.

250 3 −8 3 250 3 −8 3

Polynomials

For the following exercises, perform the given operations and simplify.

35.

(3 x 3 +2x1)+(4 x 2 2x+7) (3 x 3 +2x1)+(4 x 2 2x+7)

36.

( 2y+1 )( 2 y 2 2y5 ) ( 2y+1 )( 2 y 2 2y5 )

37.

(2 x 2 +3x6)+(3 x 2 4x+9) (2 x 2 +3x6)+(3 x 2 4x+9)

38.

( 6 a 2 +3a+10 )( 6 a 2 −3a+5 ) ( 6 a 2 +3a+10 )( 6 a 2 −3a+5 )

39.

(k+3)(k6) (k+3)(k6)

40.

(2h+1)(3h2) (2h+1)(3h2)

41.

( x+1 )( x 2 +1 ) ( x+1 )( x 2 +1 )

42.

(m2)( m 2 +2m3) (m2)( m 2 +2m3)

43.

( a+2b )( 3ab ) ( a+2b )( 3ab )

44.

( x+y )( xy ) ( x+y )( xy )

Factoring Polynomials

For the following exercises, find the greatest common factor.

45.

81p+9pq27 p 2 q 2 81p+9pq27 p 2 q 2

46.

12 x 2 y+4x y 2 −18xy 12 x 2 y+4x y 2 −18xy

47.

88 a 3 b+4 a 2 b144 a 2 88 a 3 b+4 a 2 b144 a 2

For the following exercises, factor the polynomial.

48.

2 x 2 9x18 2 x 2 9x18

49.

8 a 2 +30a27 8 a 2 +30a27

50.

d 2 5d66 d 2 5d66

51.

x 2 +10x+25 x 2 +10x+25

52.

y 2 6y+9 y 2 6y+9

53.

4 h 2 12hk+9 k 2 4 h 2 12hk+9 k 2

54.

361 x 2 121 361 x 2 121

55.

p 3 +216 p 3 +216

56.

8 x 3 125 8 x 3 125

57.

64 q 3 27 p 3 64 q 3 27 p 3

58.

4x (x1) 1 4 +3 (x1) 3 4 4x (x1) 1 4 +3 (x1) 3 4

59.

3p ( p+3 ) 1 3 −8 ( p+3 ) 4 3 3p ( p+3 ) 1 3 −8 ( p+3 ) 4 3

60.

4r ( 2r1 ) 2 3 5 ( 2r1 ) 1 3 4r ( 2r1 ) 2 3 5 ( 2r1 ) 1 3

Rational Expressions

For the following exercises, simplify the expression.

61.

x 2 x12 x 2 8x+16 x 2 x12 x 2 8x+16

62.

4 y 2 25 4 y 2 20y+25 4 y 2 25 4 y 2 20y+25

63.

2 a 2 a3 2 a 2 6a8 5 a 2 19a4 10 a 2 13a3 2 a 2 a3 2 a 2 6a8 5 a 2 19a4 10 a 2 13a3

64.

d4 d 2 9 d3 d 2 16 d4 d 2 9 d3 d 2 16

65.

m 2 +5m+6 2 m 2 5m3 ÷ 2 m 2 +3m9 4 m 2 4m3 m 2 +5m+6 2 m 2 5m3 ÷ 2 m 2 +3m9 4 m 2 4m3

66.

4 d 2 7d2 6 d 2 17d+10 ÷ 8 d 2 +6d+1 6 d 2 +7d10 4 d 2 7d2 6 d 2 17d+10 ÷ 8 d 2 +6d+1 6 d 2 +7d10

67.

10 x + 6 y 10 x + 6 y

68.

12 a 2 +2a+1 3 a 2 −1 12 a 2 +2a+1 3 a 2 −1

69.

1 d + 2 c 6c+12d dc 1 d + 2 c 6c+12d dc

70.

3 x 7 y 2 x 3 x 7 y 2 x


1.9.1: Review Exercises is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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