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Elementary Algebra

Chapter 7

Elementary AlgebraChapter 7

Try It

7.1

16

7.2

2

7.3

6 x 2 6 x 2

7.4

8 y 2 8 y 2

7.5

2 a b 2 a b

7.6

3 m 3 n 3 m 3 n

7.7

5 m 2 5 m 2

7.8

7 x 7 x

7.9

6 ( a + 4 ) 6 ( a + 4 )

7.10

2 ( b + 7 ) 2 ( b + 7 )

7.11

14 ( x + 1 ) 14 ( x + 1 )

7.12

12 ( p + 1 ) 12 ( p + 1 )

7.13

8 ( u 2 ) 8 ( u 2 )

7.14

30 ( y 2 ) 30 ( y 2 )

7.15

5 ( x 2 5 x + 3 ) 5 ( x 2 5 x + 3 )

7.16

3 ( y 2 4 y + 9 ) 3 ( y 2 4 y + 9 )

7.17

2 x 2 ( x + 6 ) 2 x 2 ( x + 6 )

7.18

3 y 2 ( 2 y 5 ) 3 y 2 ( 2 y 5 )

7.19

2 x ( 10 x 2 5 x + 7 ) 2 x ( 10 x 2 5 x + 7 )

7.20

4 y ( 6 y 2 3 y 5 ) 4 y ( 6 y 2 3 y 5 )

7.21

3 y 2 ( 3 x + 2 x 2 + 7 y ) 3 y 2 ( 3 x + 2 x 2 + 7 y )

7.22

3 p ( p 2 2 p q + 3 q 2 ) 3 p ( p 2 2 p q + 3 q 2 )

7.23

−8 ( 8 z + 8 ) −8 ( 8 z + 8 )

7.24

−9 ( y + 3 ) −9 ( y + 3 )

7.25

−4 b ( b 4 ) −4 b ( b 4 )

7.26

−7 a ( a 3 ) −7 a ( a 3 )

7.27

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

7.28

( n 4 ) ( 8 n + 5 ) ( n 4 ) ( 8 n + 5 )

7.29

( x + 8 ) ( y + 3 ) ( x + 8 ) ( y + 3 )

7.30

( a + 7 ) ( b + 8 ) ( a + 7 ) ( b + 8 )

7.31

( x 5 ) ( x + 2 ) ( x 5 ) ( x + 2 )

7.32

( y + 4 ) ( y 7 ) ( y + 4 ) ( y 7 )

7.33

( x + 2 ) ( x + 4 ) ( x + 2 ) ( x + 4 )

7.34

( y + 3 ) ( y + 5 ) ( y + 3 ) ( y + 5 )

7.35

( q + 4 ) ( q + 6 ) ( q + 4 ) ( q + 6 )

7.36

( t + 2 ) ( t + 12 ) ( t + 2 ) ( t + 12 )

7.37

( x + 4 ) ( x + 15 ) ( x + 4 ) ( x + 15 )

7.38

( v + 3 ) ( v + 20 ) ( v + 3 ) ( v + 20 )

7.39

( u 3 ) ( u 6 ) ( u 3 ) ( u 6 )

7.40

( y 7 ) ( y 9 ) ( y 7 ) ( y 9 )

7.41

( h 2 ) ( h + 6 ) ( h 2 ) ( h + 6 )

7.42

( k 4 ) ( k + 5 ) ( k 4 ) ( k + 5 )

7.43

( x + 2 ) ( x 6 ) ( x + 2 ) ( x 6 )

7.44

( y + 4 ) ( y 5 ) ( y + 4 ) ( y 5 )

7.45

( r + 5 ) ( r 8 ) ( r + 5 ) ( r 8 )

7.46

( s + 2 ) ( s 5 ) ( s + 2 ) ( s 5 )

7.47

prime

7.48

prime

7.49

( m + 3 ) ( m + 6 ) ( m + 3 ) ( m + 6 )

7.50

( n 3 ) ( n 4 ) ( n 3 ) ( n 4 )

7.51

( u + 4 v ) ( u + 7 v ) ( u + 4 v ) ( u + 7 v )

7.52

( x + 6 y ) ( x + 7 y ) ( x + 6 y ) ( x + 7 y )

7.53

( a b ) ( a 10 b ) ( a b ) ( a 10 b )

7.54

( m n ) ( m 12 n ) ( m n ) ( m 12 n )

7.55

prime

7.56

prime

7.57

no method undo using FOIL factor with grouping

7.58

factor using grouping no method undo using FOIL

7.59

4 ( m + 1 ) ( m 2 ) 4 ( m + 1 ) ( m 2 )

7.60

5 ( k + 2 ) ( k 5 ) 5 ( k + 2 ) ( k 5 )

7.61

3 ( r 1 ) ( r 2 ) 3 ( r 1 ) ( r 2 )

7.62

2 ( t 2 ) ( t 3 ) 2 ( t 2 ) ( t 3 )

7.63

5 x ( x 1 ) ( x + 4 ) 5 x ( x 1 ) ( x + 4 )

7.64

6 y ( y 2 ) ( y + 5 ) 6 y ( y 2 ) ( y + 5 )

7.65

( a + 1 ) ( 2 a + 3 ) ( a + 1 ) ( 2 a + 3 )

7.66

( b + 1 ) ( 4 b + 1 ) ( b + 1 ) ( 4 b + 1 )

7.67

( 2 x 3 ) ( 4 x 1 ) ( 2 x 3 ) ( 4 x 1 )

7.68

( 2 y 7 ) ( 5 y 1 ) ( 2 y 7 ) ( 5 y 1 )

7.69

( a 1 ) ( 8 a + 5 ) ( a 1 ) ( 8 a + 5 )

7.70

( 2 b + 3 ) ( 3 b 5 ) ( 2 b + 3 ) ( 3 b 5 )

7.71

( 3 x + 2 ) ( 6 x 5 ) ( 3 x + 2 ) ( 6 x 5 )

7.72

( 3 y + 1 ) ( 10 y 21 ) ( 3 y + 1 ) ( 10 y 21 )

7.73

5 n ( n 4 ) ( 3 n 5 ) 5 n ( n 4 ) ( 3 n 5 )

7.74

8 q ( q + 6 ) ( 7 q 2 ) 8 q ( q + 6 ) ( 7 q 2 )

7.75

( x + 2 ) ( 6 x + 1 ) ( x + 2 ) ( 6 x + 1 )

7.76

( 2 y + 1 ) ( 2 y + 3 ) ( 2 y + 1 ) ( 2 y + 3 )

7.77

( 4 h 5 ) ( 5 h + 3 ) ( 4 h 5 ) ( 5 h + 3 )

7.78

( q + 4 ) ( 6 q 5 ) ( q + 4 ) ( 6 q 5 )

7.79

( 2 t + 5 ) ( 5 t 3 ) ( 2 t + 5 ) ( 5 t 3 )

7.80

( u + 1 ) ( 3 u + 5 ) ( u + 1 ) ( 3 u + 5 )

7.81

4 ( 2 x 3 ) ( 2 x 1 ) 4 ( 2 x 3 ) ( 2 x 1 )

7.82

3 ( 3 w 2 ) ( 2 w 3 ) 3 ( 3 w 2 ) ( 2 w 3 )

7.83

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

7.84

( 3 y + 4 ) 2 ( 3 y + 4 ) 2

7.85

( 8 y 5 ) 2 ( 8 y 5 ) 2

7.86

( 4 z 9 ) 2 ( 4 z 9 ) 2

7.87

( 7 x + 6 y ) 2 ( 7 x + 6 y ) 2

7.88

( 8 m + 7 n ) 2 ( 8 m + 7 n ) 2

7.89

( 8 r + 3 s ) ( 2 r + 3 s ) ( 8 r + 3 s ) ( 2 r + 3 s )

7.90

( 3 u + 4 ) ( 3 u + 25 ) ( 3 u + 4 ) ( 3 u + 25 )

7.91

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

7.92

3 q ( 3 p + 5 ) 2 3 q ( 3 p + 5 ) 2

7.93

( h 9 ) ( h + 9 ) ( h 9 ) ( h + 9 )

7.94

( k 11 ) ( k + 11 ) ( k 11 ) ( k + 11 )

7.95

( m 1 ) ( m + 1 ) ( m 1 ) ( m + 1 )

7.96

( 9 y 1 ) ( 9 y + 1 ) ( 9 y 1 ) ( 9 y + 1 )

7.97

( 16 m 5 n ) ( 16 m + 5 n ) ( 16 m 5 n ) ( 16 m + 5 n )

7.98

( 12 p 3 q ) ( 12 p + 3 q ) ( 12 p 3 q ) ( 12 p + 3 q )

7.99

( 12 x ) ( 12 + x ) ( 12 x ) ( 12 + x )

7.100

( 13 p ) ( 13 + p ) ( 13 p ) ( 13 + p )

7.101

( a 2 + b 2 ) ( a + b ) ( a b ) ( a 2 + b 2 ) ( a + b ) ( a b )

7.102

( x 2 + 4 ) ( x + 2 ) ( x 2 ) ( x 2 + 4 ) ( x + 2 ) ( x 2 )

7.103

7 x ( y 5 ) ( y + 5 ) 7 x ( y 5 ) ( y + 5 )

7.104

5 b ( 3 a 4 ) ( 3 a + 4 ) 5 b ( 3 a 4 ) ( 3 a + 4 )

7.105

8 ( a 2 + 25 ) 8 ( a 2 + 25 )

7.106

9 ( 4 y 2 + 9 ) 9 ( 4 y 2 + 9 )

7.107

( x + 3 ) ( x 2 3 x + 9 ) ( x + 3 ) ( x 2 3 x + 9 )

7.108

( y + 2 ) ( y 2 2 y + 4 ) ( y + 2 ) ( y 2 2 y + 4 )

7.109

( u 5 ) ( u 2 + 5 u + 25 ) ( u 5 ) ( u 2 + 5 u + 25 )

7.110

( v 7 ) ( v 2 + 7 v + 49 ) ( v 7 ) ( v 2 + 7 v + 49 )

7.111

( 4 3 x ) ( 16 + 12 x + 9 x 2 ) ( 4 3 x ) ( 16 + 12 x + 9 x 2 )

7.112

( 3 2 y ) ( 9 + 6 y + 4 y 2 ) ( 3 2 y ) ( 9 + 6 y + 4 y 2 )

7.113

( 2 x 3 y ) ( 4 x 2 + 6 x y + 9 y 2 ) ( 2 x 3 y ) ( 4 x 2 + 6 x y + 9 y 2 )

7.114

( 10 m 5 n ) ( 100 m 2 50 m n + 25 n 2 ) ( 10 m 5 n ) ( 100 m 2 50 m n + 25 n 2 )

7.115

4 ( 5 p + q ) ( 25 p 2 5 p q + q 2 ) 4 ( 5 p + q ) ( 25 p 2 5 p q + q 2 )

7.116

2 ( 6 c + 7 d ) ( 36 c 2 42 c d + 49 d 2 ) 2 ( 6 c + 7 d ) ( 36 c 2 42 c d + 49 d 2 )

7.117

3 a 3 ( a + 6 ) 3 a 3 ( a + 6 )

7.118

9 b 5 ( 5 b + 3 ) 9 b 5 ( 5 b + 3 )

7.119

( 5 a 6 ) ( 2 a 1 ) ( 5 a 6 ) ( 2 a 1 )

7.120

( 2 x 3 ) ( 4 x 3 ) ( 2 x 3 ) ( 4 x 3 )

7.121

x ( x 2 + 36 ) x ( x 2 + 36 )

7.122

3 ( 9 y 2 + 16 ) 3 ( 9 y 2 + 16 )

7.123

4 x ( 2 x 3 ) ( 2 x + 3 ) 4 x ( 2 x 3 ) ( 2 x + 3 )

7.124

3 ( 3 y 4 ) ( 3 y + 4 ) 3 ( 3 y 4 ) ( 3 y + 4 )

7.125

( 2 x + 5 y ) 2 ( 2 x + 5 y ) 2

7.126

( 3 m + 7 n ) 2 ( 3 m + 7 n ) 2

7.127

8 ( y 1 ) ( y + 3 ) 8 ( y 1 ) ( y + 3 )

7.128

5 ( u 9 ) ( u + 6 ) 5 ( u 9 ) ( u + 6 )

7.129

2 ( 5 m + 6 ) ( 25 m 2 30 m + 36 ) 2 ( 5 m + 6 ) ( 25 m 2 30 m + 36 )

7.130

3 ( 3 q + 4 ) ( 9 q 2 12 q + 16 ) 3 ( 3 q + 4 ) ( 9 q 2 12 q + 16 )

7.131

4 ( a 2 + 4 ) ( a 2 ) ( a + 2 ) 4 ( a 2 + 4 ) ( a 2 ) ( a + 2 )

7.132

7 ( y 2 + 1 ) ( y 1 ) ( y + 1 ) 7 ( y 2 + 1 ) ( y 1 ) ( y + 1 )

7.133

6 ( x + b ) ( x 2 c ) 6 ( x + b ) ( x 2 c )

7.134

2 ( 4 x 1 ) ( x + 3 y ) 2 ( 4 x 1 ) ( x + 3 y )

7.135

4 ( p 1 ) ( p 3 ) 4 ( p 1 ) ( p 3 )

7.136

3 ( q 2 ) ( 2 q + 1 ) 3 ( q 2 ) ( 2 q + 1 )

7.137

x = 3 , x = −5 x = 3 , x = −5

7.138

y = 6 , y = −9 y = 6 , y = −9

7.139

m = 2 3 , m = 1 2 m = 2 3 , m = 1 2

7.140

p = 3 4 , p = 3 4 p = 3 4 , p = 3 4

7.141

u = 0 , u = 1 5 u = 0 , u = 1 5

7.142

w = 0 , w = 3 2 w = 0 , w = 3 2

7.143

x = 1 x = 1

7.144

v = 2 v = 2

7.145

x = 4 , x = −3 x = 4 , x = −3

7.146

b = −2 , b = −7 b = −2 , b = −7

7.147

c = 0 , c = 4 3 c = 0 , c = 4 3

7.148

d = 3 , d = 1 2 d = 3 , d = 1 2

7.149

a = 0 , a = −1 a = 0 , a = −1

7.150

b = 0 , b = 1 3 b = 0 , b = 1 3

7.151

p = 7 5 , p = 7 5 p = 7 5 , p = 7 5

7.152

x = 11 6 , x = 11 6 x = 11 6 , x = 11 6

7.153

m = 1 , m = 3 2 m = 1 , m = 3 2

7.154

k = 3 , k = −3 k = 3 , k = −3

7.155

x = 0 , x = 3 2 x = 0 , x = 3 2

7.156

y = 0 , y = 1 4 y = 0 , y = 1 4

7.157

a = 5 2 , a = 2 3 a = 5 2 , a = 2 3

7.158

b = 2 , b = 1 20 b = 2 , b = 1 20

7.159

−15 , −16 and 15 , 16 −15 , −16 and 15 , 16

7.160

−21 , −20 and 20 , 21 −21 , −20 and 20 , 21

7.161

55 feet and 66 feet

7.162

1212 feet and 1515 feet

7.163

55 feet and 1212 feet

7.164

2424 feet and 2525 feet

Section 7.1 Exercises

1.

2

3.

18

5.

10

7.

x x

9.

8 w 2 8 w 2

11.

2 p q 2 p q

13.

6 m 2 n 3 6 m 2 n 3

15.

2 a 2 a

17.

5 x 3 5 x 3

19.

4 ( x + 5 ) 4 ( x + 5 )

21.

3 ( 2 m + 3 ) 3 ( 2 m + 3 )

23.

9 ( q + 1 ) 9 ( q + 1 )

25.

8 ( m 1 ) 8 ( m 1 )

27.

9 ( n 7 ) 9 ( n 7 )

29.

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

31.

2 ( 4 p 2 + 2 p + 1 ) 2 ( 4 p 2 + 2 p + 1 )

33.

8 y 2 ( y + 2 ) 8 y 2 ( y + 2 )

35.

5 x ( x 2 3 x + 4 ) 5 x ( x 2 3 x + 4 )

37.

6 y 2 ( 2 x + 3 x 2 5 y ) 6 y 2 ( 2 x + 3 x 2 5 y )

39.

−2 ( x + 2 ) −2 ( x + 2 )

41.

( x + 1 ) ( 5 x + 3 ) ( x + 1 ) ( 5 x + 3 )

43.

( b 2 ) ( 3 b 13 ) ( b 2 ) ( 3 b 13 )

45.

( y + 3 ) ( x + 2 ) ( y + 3 ) ( x + 2 )

47.

( u + 2 ) ( v 9 ) ( u + 2 ) ( v 9 )

49.

( b 4 ) ( b + 5 ) ( b 4 ) ( b + 5 )

51.

( p 9 ) ( p + 4 ) ( p 9 ) ( p + 4 )

53.

−10 ( 2 x + 1 ) −10 ( 2 x + 1 )

55.

( x 2 + 2 ) ( 3 x 7 ) ( x 2 + 2 ) ( 3 x 7 )

57.

( x + y ) ( x + 5 ) ( x + y ) ( x + 5 )

59.

w ( w 6 ) w ( w 6 )

61.

Answers will vary.

Section 7.2 Exercises

63.

( x + 1 ) ( x + 3 ) ( x + 1 ) ( x + 3 )

65.

( m + 1 ) ( m + 11 ) ( m + 1 ) ( m + 11 )

67.

( a + 4 ) ( a + 5 ) ( a + 4 ) ( a + 5 )

69.

( p + 5 ) ( p + 6 ) ( p + 5 ) ( p + 6 )

71.

( n + 3 ) ( n + 16 ) ( n + 3 ) ( n + 16 )

73.

( a + 5 ) ( a + 20 ) ( a + 5 ) ( a + 20 )

75.

( x 2 ) ( x 6 ) ( x 2 ) ( x 6 )

77.

( y 3 ) ( y 15 ) ( y 3 ) ( y 15 )

79.

( x 1 ) ( x 7 ) ( x 1 ) ( x 7 )

81.

( p 1 ) ( p + 6 ) ( p 1 ) ( p + 6 )

83.

( y + 1 ) ( y 7 ) ( y + 1 ) ( y 7 )

85.

( x 4 ) ( x + 3 ) ( x 4 ) ( x + 3 )

87.

( a 7 ) ( a + 4 ) ( a 7 ) ( a + 4 )

89.

( w 9 ) ( w + 4 ) ( w 9 ) ( w + 4 )

91.

prime

93.

( x 4 ) ( x 2 ) ( x 4 ) ( x 2 )

95.

( x 12 ) ( x + 1 ) ( x 12 ) ( x + 1 )

97.

( p + q ) ( p + 2 q ) ( p + q ) ( p + 2 q )

99.

( r + 3 s ) ( r + 12 s ) ( r + 3 s ) ( r + 12 s )

101.

( m 2 n ) ( m 10 n ) ( m 2 n ) ( m 10 n )

103.

( x + 8 y ) ( x 10 y ) ( x + 8 y ) ( x 10 y )

105.

( m + n ) ( m 65 n ) ( m + n ) ( m 65 n )

107.

( a + 8 b ) ( a 3 b ) ( a + 8 b ) ( a 3 b )

109.

prime

111.

prime

113.

( u 6 ) ( u 6 ) ( u 6 ) ( u 6 )

115.

( x + 2 ) ( x 16 ) ( x + 2 ) ( x 16 )

117.

( r 4 s ) ( r 16 s ) ( r 4 s ) ( r 16 s )

119.

( k + 4 ) ( k + 30 ) ( k + 4 ) ( k + 30 )

121.

prime

123.

( m + 8 n ) ( m 7 n ) ( m + 8 n ) ( m 7 n )

125.

( u 15 v ) ( u 2 v ) ( u 15 v ) ( u 2 v )

127.

prime

129.

( x + 8 ) ( x 7 ) ( x + 8 ) ( x 7 )

131.

Answers may vary

133.

Answers may vary

Section 7.3 Exercises

135.

factor the GCF, binomial Undo FOIL factor by grouping

137.

undo FOIL factor by grouping factor the GCF, binomial

139.

5 ( x + 1 ) ( x + 6 ) 5 ( x + 1 ) ( x + 6 )

141.

2 ( z 4 ) ( z + 3 ) 2 ( z 4 ) ( z + 3 )

143.

7 ( v 1 ) ( v 8 ) 7 ( v 1 ) ( v 8 )

145.

p ( p 10 ) ( p + 2 ) p ( p 10 ) ( p + 2 )

147.

3 m ( m 5 ) ( m 2 ) 3 m ( m 5 ) ( m 2 )

149.

5 x 2 ( x 3 ) ( x + 5 ) 5 x 2 ( x 3 ) ( x + 5 )

151.

( 2 t + 5 ) ( t + 1 ) ( 2 t + 5 ) ( t + 1 )

153.

( 11 x + 1 ) ( x + 3 ) ( 11 x + 1 ) ( x + 3 )

155.

( 4 w 1 ) ( w 1 ) ( 4 w 1 ) ( w 1 )

157.

( 3 p 2 ) ( 2 p 5 ) ( 3 p 2 ) ( 2 p 5 )

159.

( 4 q + 1 ) ( q 2 ) ( 4 q + 1 ) ( q 2 )

161.

( 4 p 3 ) ( p + 5 ) ( 4 p 3 ) ( p + 5 )

163.

16 ( x 1 ) ( x 1 ) 16 ( x 1 ) ( x 1 )

165.

10 q ( 3 q + 2 ) ( q + 4 ) 10 q ( 3 q + 2 ) ( q + 4 )

167.

( 5 n + 1 ) ( n + 4 ) ( 5 n + 1 ) ( n + 4 )

169.

( 3 z + 1 ) ( 3 z + 4 ) ( 3 z + 1 ) ( 3 z + 4 )

171.

( 2 k 3 ) ( 2 k 5 ) ( 2 k 3 ) ( 2 k 5 )

173.

( 5 s 4 ) ( s 1 ) ( 5 s 4 ) ( s 1 )

175.

( 3 y + 5 ) ( 2 y 3 ) ( 3 y + 5 ) ( 2 y 3 )

177.

( 2 n + 3 ) ( n 15 ) ( 2 n + 3 ) ( n 15 )

179.

prime

181.

10 ( 6 y 1 ) ( y + 5 ) 10 ( 6 y 1 ) ( y + 5 )

183.

3 z ( 8 z + 3 ) ( 2 z 5 ) 3 z ( 8 z + 3 ) ( 2 z 5 )

185.

8 ( 2 s + 3 ) ( s + 1 ) 8 ( 2 s + 3 ) ( s + 1 )

187.

12 ( 4 y 3 ) ( y + 1 ) 12 ( 4 y 3 ) ( y + 1 )

189.

( 4 y 7 ) ( 3 y 2 ) ( 4 y 7 ) ( 3 y 2 )

191.

( a 5 ) ( a + 4 ) ( a 5 ) ( a + 4 )

193.

( 2 n 1 ) ( 3 n + 4 ) ( 2 n 1 ) ( 3 n + 4 )

195.

prime

197.

13 ( z 2 + 3 z 2 ) 13 ( z 2 + 3 z 2 )

199.

( x + 7 ) ( x 4 ) ( x + 7 ) ( x 4 )

201.

3 p ( p + 7 ) 3 p ( p + 7 )

203.

6 ( r + 2 ) ( r + 3 ) 6 ( r + 2 ) ( r + 3 )

205.

4 ( 2 n + 1 ) ( 3 n + 1 ) 4 ( 2 n + 1 ) ( 3 n + 1 )

207.

( x + 6 ) ( x 4 ) ( x + 6 ) ( x 4 )

209.

−16 ( t 6 ) ( t + 1 ) −16 ( t 6 ) ( t + 1 )

211.

Answers may vary.

213.

Answers may vary.

Section 7.4 Exercises

215.

( 4 y + 3 ) 2 ( 4 y + 3 ) 2

217.

( 6 s + 7 ) 2 ( 6 s + 7 ) 2

219.

( 10 x 1 ) 2 ( 10 x 1 ) 2

221.

( 5 n 12 ) 2 ( 5 n 12 ) 2

223.

( 7 x 2 y ) 2 ( 7 x 2 y ) 2

225.

( 5 n + 4 ) ( 5 n + 1 ) ( 5 n + 4 ) ( 5 n + 1 )

227.

(8m1)2(8m1)2

229.

10 ( k + 4 ) 2 10 ( k + 4 ) 2

231.

3 u ( 5 u v ) 2 3 u ( 5 u v ) 2

233.

( x 4 ) ( x + 4 ) ( x 4 ) ( x + 4 )

235.

( 5 v 1 ) ( 5 v + 1 ) ( 5 v 1 ) ( 5 v + 1 )

237.

( 11 x 12 y ) ( 11 x + 12 y ) ( 11 x 12 y ) ( 11 x + 12 y )

239.

( 13 c 6 d ) ( 13 c + 6 d ) ( 13 c 6 d ) ( 13 c + 6 d )

241.

(7x2)(7x+2)(7x2)(7x+2) (27x)(2+7x)(27x)(2+7x)

243.

( 2 z 1 ) ( 2 z + 1 ) ( 4 z 2 + 1 ) ( 2 z 1 ) ( 2 z + 1 ) ( 4 z 2 + 1 )

245.

5 ( q 3 ) ( q + 3 ) 5 ( q 3 ) ( q + 3 )

247.

6 ( 4 p 2 + 9 ) 6 ( 4 p 2 + 9 )

249.

( x + 5 ) ( x 2 5 x + 25 ) ( x + 5 ) ( x 2 5 x + 25 )

251.

( z 3 ) ( z 2 + 3 z + 9 ) ( z 3 ) ( z 2 + 3 z + 9 )

253.

( 2 7 t ) ( 4 + 14 t + 49 t 2 ) ( 2 7 t ) ( 4 + 14 t + 49 t 2 )

255.

( 2 y 5 z ) ( 4 y 2 + 10 y z + 25 z 2 ) ( 2 y 5 z ) ( 4 y 2 + 10 y z + 25 z 2 )

257.

7 ( k + 2 ) ( k 2 2 k + 4 ) 7 ( k + 2 ) ( k 2 2 k + 4 )

259.

2 ( 1 2 y ) ( 1 + 2 y + 4 y 2 ) 2 ( 1 2 y ) ( 1 + 2 y + 4 y 2 )

261.

( 8 a 5 ) ( 8 a + 5 ) ( 8 a 5 ) ( 8 a + 5 )

263.

3 ( 3 q 1 ) ( 3 q + 1 ) 3 ( 3 q 1 ) ( 3 q + 1 )

265.

( 4 x 9 ) 2 ( 4 x 9 ) 2

267.

2 ( 4 p 2 + 1 ) 2 ( 4 p 2 + 1 )

269.

( 5 2 y ) ( 25 + 10 y + 4 y 2 ) ( 5 2 y ) ( 25 + 10 y + 4 y 2 )

271.

5 ( 3 n + 2 ) 2 5 ( 3 n + 2 ) 2

273.

( 2 w + 15 ) 2 ( 2 w + 15 ) 2

275.

Answers may vary.

277.

Answers may vary.

Section 7.5 Exercises

279.

5 x 3 ( 2 x + 7 ) 5 x 3 ( 2 x + 7 )

281.

( y 3 ) ( y + 13 ) ( y 3 ) ( y + 13 )

283.

( 2 n 1 ) ( n + 7 ) ( 2 n 1 ) ( n + 7 )

285.

a 3 ( a 2 + 9 ) a 3 ( a 2 + 9 )

287.

( 11 r s ) ( 11 r + s ) ( 11 r s ) ( 11 r + s )

289.

8 ( m 2 ) ( m + 2 ) 8 ( m 2 ) ( m + 2 )

291.

( 5 w 6 ) 2 ( 5 w 6 ) 2

293.

( m + 7 n ) 2 ( m + 7 n ) 2

295.

7 ( b + 3 ) ( b 2 ) 7 ( b + 3 ) ( b 2 )

297.

3 ( x 3 ) ( x 2 + 3 x + 9 ) 3 ( x 3 ) ( x 2 + 3 x + 9 )

299.

( k 2 ) ( k + 2 ) ( k 2 + 4 ) ( k 2 ) ( k + 2 ) ( k 2 + 4 )

301.

3 ( 5 p + 4 ) ( q 1 ) 3 ( 5 p + 4 ) ( q 1 )

303.

4 ( x + 3 ) ( x + 7 ) 4 ( x + 3 ) ( x + 7 )

305.

u 2 ( u + 1 ) ( u 2 u + 1 ) u 2 ( u + 1 ) ( u 2 u + 1 )

307.

prime

309.

10 ( m 5 ) ( m + 5 ) ( m 2 + 25 ) 10 ( m 5 ) ( m + 5 ) ( m 2 + 25 )

311.

−16(t25)−16(t25) −8(2t+5)(t2)−8(2t+5)(t2)

Section 7.6 Exercises

315.

x = 3 , x = −7 x = 3 , x = −7

317.

a = 10 / 3 , a = 7 / 2 a = 10 / 3 , a = 7 / 2

319.

m = 0 , m = 5 / 12 m = 0 , m = 5 / 12

321.

y = 3 y = 3

323.

x = 1 / 2 x = 1 / 2

325.

x = −3 , x = −4 x = −3 , x = −4

327.

a = −4 / 5 , a = 6 a = −4 / 5 , a = 6

329.

m = 5 / 4 , m = 3 m = 5 / 4 , m = 3

331.

a = −1 , a = 0 a = −1 , a = 0

333.

m = 12 / 7 , m = −12 / 7 m = 12 / 7 , m = −12 / 7

335.

y = −1 , y = 6 y = −1 , y = 6

337.

x = 3 / 2 , x = −1 x = 3 / 2 , x = −1

339.

p = 0 , p = ¾ p = 0 , p = ¾

341.

x = 3 / 2 x = 3 / 2

343.

7 and 8 ; 8 and −7 7 and 8 ; 8 and −7

345.

4 feet and 7 feet 4 feet and 7 feet

347.

6 feet and 8 feet 6 feet and 8 feet

349.

x = −8 , x = 3 x = −8 , x = 3

351.

p = −1 , p = −11 p = −1 , p = −11

353.

m = −2 , m = 8 m = −2 , m = 8

355.

a = 0 , a = −6 , a = 7 a = 0 , a = −6 , a = 7

357.

10 and 11 ; 11 and −10 10 and 11 ; 11 and −10

359.

10 feet

361.

Answers may vary.

Review Exercises

363.

6

365.

15 15

367.

6 ( 4 x 7 ) 6 ( 4 x 7 )

369.

3 m 2 ( 5 m 2 + 2 n ) 3 m 2 ( 5 m 2 + 2 n )

371.

( a + b ) ( x y ) ( a + b ) ( x y )

373.

( x 3 ) ( x + 7 ) ( x 3 ) ( x + 7 )

375.

( m 2 + 1 ) ( m + 1 ) ( m 2 + 1 ) ( m + 1 )

377.

( u + 8 ) ( u + 9 ) ( u + 8 ) ( u + 9 )

379.

( k 6 ) ( k 10 ) ( k 6 ) ( k 10 )

381.

( y + 7 ) ( y 1 ) ( y + 7 ) ( y 1 )

383.

( s 4 ) ( s + 2 ) ( s 4 ) ( s + 2 )

385.

( x + 5 y ) ( x + 7 y ) ( x + 5 y ) ( x + 7 y )

387.

( a + 7 b ) ( a 3 b ) ( a + 7 b ) ( a 3 b )

389.

Undo FOIL

391.

Factor the GCF

393.

6 ( x + 2 ) ( x + 5 ) 6 ( x + 2 ) ( x + 5 )

395.

3 n 2 ( n 8 ) ( n + 4 ) 3 n 2 ( n 8 ) ( n + 4 )

397.

( x + 4 ) ( 2 x + 1 ) ( x + 4 ) ( 2 x + 1 )

399.

( 3 a 1 ) ( 6 a 1 ) ( 3 a 1 ) ( 6 a 1 )

401.

( 5 p + 4 ) ( 3 p 2 ) ( 5 p + 4 ) ( 3 p 2 )

403.

( 5 s 2 ) ( 8 s + 3 ) ( 5 s 2 ) ( 8 s + 3 )

405.

3 ( x + 4 ) ( x 3 ) 3 ( x + 4 ) ( x 3 )

407.

5 ( 4 y + 1 ) ( 3 y 5 ) 5 ( 4 y + 1 ) ( 3 y 5 )

409.

( 5 x + 3 ) 2 ( 5 x + 3 ) 2

411.

( 6 a 7 b ) 2 ( 6 a 7 b ) 2

413.

10 ( 2 x + 9 ) 2 10 ( 2 x + 9 ) 2

415.

2 y ( y 4 ) 2 2 y ( y 4 ) 2

417.

( 9 r 5 ) ( 9 r + 5 ) ( 9 r 5 ) ( 9 r + 5 )

419.

( 13 m + n ) ( 13 m n ) ( 13 m + n ) ( 13 m n )

421.

( 5 p 1 ) ( 5 p + 1 ) ( 5 p 1 ) ( 5 p + 1 )

423.

( 3 + 11 y ) ( 3 11 y ) ( 3 + 11 y ) ( 3 11 y )

425.

5 ( 2 x 5 ) ( 2 x + 5 ) 5 ( 2 x 5 ) ( 2 x + 5 )

427.

u ( 7 u + 3 ) ( 7 u 3 ) u ( 7 u + 3 ) ( 7 u 3 )

429.

( a 5 ) ( a 2 + 5 a + 25 ) ( a 5 ) ( a 2 + 5 a + 25 )

431.

2 ( m + 3 ) ( m 2 3 m + 9 ) 2 ( m + 3 ) ( m 2 3 m + 9 )

433.

4 x 2 ( 6 x + 11 ) 4 x 2 ( 6 x + 11 )

435.

( 4 n 7 m ) 2 ( 4 n 7 m ) 2

437.

( r + 6 ) ( 5 r 8 ) ( r + 6 ) ( 5 r 8 )

439.

( n 2 + 9 ) ( n + 3 ) ( n 3 ) ( n 2 + 9 ) ( n + 3 ) ( n 3 )

441.

5 ( x 3 ) ( x + 4 ) 5 ( x 3 ) ( x + 4 )

443.

( m + 5 ) ( m 2 5 m + 25 ) ( m + 5 ) ( m 2 5 m + 25 )

445.

a = 3 a = −7 a = 3 a = −7

447.

m = 0 m = 5 2 m = –6 m = 0 m = 5 2 m = –6

449.

x = −4 , x = −5 x = −4 , x = −5

451.

p = 5 2 , p = 8 p = 5 2 , p = 8

453.

m = 5 12 , m = 5 12 m = 5 12 , m = 5 12

455.

−21 , −22 21 , 22 −21 , −22 21 , 22

Practice Test

457.

7 ( y 6 ) 7 ( y 6 )

459.

40 a 2 ( 2 + 3 a ) 40 a 2 ( 2 + 3 a )

461.

( x + 7 ) ( x + 6 ) ( x + 7 ) ( x + 6 )

463.

3 a ( a + 4 ) ( a 6 ) 3 a ( a + 4 ) ( a 6 )

465.

5 ( n + 3 ) 2 5 ( n + 3 ) 2

467.

( x 8 ) ( y + 7 ) ( x 8 ) ( y + 7 )

469.

( 3 s 2 ) 2 ( 3 s 2 ) 2

471.

( 10 a ) ( 10 + a ) ( 10 a ) ( 10 + a )

473.

3 ( x + 5 y ) ( x 5 y ) 3 ( x + 5 y ) ( x 5 y )

475.

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

477.

( 4 m + 1 ) ( 2 m + 5 ) ( 4 m + 1 ) ( 2 m + 5 )

479.

y = −11 , y = 12 y = −11 , y = 12

481.

b = 1 , b = −1 b = 1 , b = −1

483.

n = 7 4 , n = −3 n = 7 4 , n = −3

485.

12 and 13 ; 13 and −12 12 and 13 ; 13 and −12

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