Contents

Chapter 7

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7.1

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7.2

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7.3

$6 x^{2} 6 x^{2}$

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7.4

$8 y^{2} 8 y^{2}$

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7.5

$2 a b 2 a b$

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7.6

$3 m^{3} n 3 m^{3} n$

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7.7

$5 m^{2} 5 m^{2}$

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7.8

$7 x 7 x$

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7.9

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

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7.10

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

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7.11

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

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7.12

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

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7.13

$8 (u - 2) 8 (u - 2)$

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7.14

$30 (y - 2) 30 (y - 2)$

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7.15

$5 (x^{2} - 5 x + 3) 5 (x^{2} - 5 x + 3)$

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7.16

$3 (y^{2} - 4 y + 9) 3 (y^{2} - 4 y + 9)$

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7.17

$2 x^{2} (x + 6) 2 x^{2} (x + 6)$

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7.18

$3 y^{2} (2 y - 5) 3 y^{2} (2 y - 5)$

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7.19

$2 x (10 x^{2} - 5 x + 7) 2 x (10 x^{2} - 5 x + 7)$

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7.20

$4 y (6 y^{2} - 3 y - 5) 4 y (6 y^{2} - 3 y - 5)$

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7.21

$3 y^{2} (3 x + 2 x^{2} + 7 y) 3 y^{2} (3 x + 2 x^{2} + 7 y)$

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7.22

$3 p (p^{2} - 2 p q + 3 q^{2}) 3 p (p^{2} - 2 p q + 3 q^{2})$

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7.23

$−8 (8 z + 8) −8 (8 z + 8)$

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7.24

$−9 (y + 3) −9 (y + 3)$

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7.25

$−4 b (b - 4) −4 b (b - 4)$

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7.26

$−7 a (a - 3) −7 a (a - 3)$

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7.27

$(m + 3) (4 m - 7) (m + 3) (4 m - 7)$

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7.28

$(n - 4) (8 n + 5) (n - 4) (8 n + 5)$

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7.29

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

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7.30

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

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7.31

$(x - 5) (x + 2) (x - 5) (x + 2)$

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7.32

$(y + 4) (y - 7) (y + 4) (y - 7)$

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7.33

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

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7.34

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

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7.35

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

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7.36

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

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7.37

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

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7.38

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

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7.39

$(u - 3) (u - 6) (u - 3) (u - 6)$

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7.40

$(y - 7) (y - 9) (y - 7) (y - 9)$

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7.41

$(h - 2) (h + 6) (h - 2) (h + 6)$

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7.42

$(k - 4) (k + 5) (k - 4) (k + 5)$

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7.43

$(x + 2) (x - 6) (x + 2) (x - 6)$

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7.44

$(y + 4) (y - 5) (y + 4) (y - 5)$

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7.45

$(r + 5) (r - 8) (r + 5) (r - 8)$

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7.46

$(s + 2) (s - 5) (s + 2) (s - 5)$

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7.47

prime

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7.48

prime

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7.49

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

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7.50

$(n - 3) (n - 4) (n - 3) (n - 4)$

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7.51

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

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7.52

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

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7.53

$(a - b) (a - 10 b) (a - b) (a - 10 b)$

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7.54

$(m - n) (m - 12 n) (m - n) (m - 12 n)$

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7.55

prime

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7.56

prime

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7.57

ⓐ no method ⓑ undo using FOIL ⓒ factor with grouping

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7.58

ⓐ factor using grouping ⓑ no method ⓒ undo using FOIL

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7.59

$4 (m + 1) (m - 2) 4 (m + 1) (m - 2)$

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7.60

$5 (k + 2) (k - 5) 5 (k + 2) (k - 5)$

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7.61

$3 (r - 1) (r - 2) 3 (r - 1) (r - 2)$

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7.62

$2 (t - 2) (t - 3) 2 (t - 2) (t - 3)$

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7.63

$5 x (x - 1) (x + 4) 5 x (x - 1) (x + 4)$

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7.64

$6 y (y - 2) (y + 5) 6 y (y - 2) (y + 5)$

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7.65

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

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7.66

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

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7.67

$(2 x - 3) (4 x - 1) (2 x - 3) (4 x - 1)$

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7.68

$(2 y - 7) (5 y - 1) (2 y - 7) (5 y - 1)$

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7.69

$(a - 1) (8 a + 5) (a - 1) (8 a + 5)$

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7.70

$(2 b + 3) (3 b - 5) (2 b + 3) (3 b - 5)$

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7.71

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

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7.72

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

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7.73

$5 n (n - 4) (3 n - 5) 5 n (n - 4) (3 n - 5)$

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7.74

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

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7.75

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

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7.76

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

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7.77

$(4 h - 5) (5 h + 3) (4 h - 5) (5 h + 3)$

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7.78

$(q + 4) (6 q - 5) (q + 4) (6 q - 5)$

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7.79

$(2 t + 5) (5 t - 3) (2 t + 5) (5 t - 3)$

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7.80

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

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7.81

$4 (2 x - 3) (2 x - 1) 4 (2 x - 3) (2 x - 1)$

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7.82

$3 (3 w - 2) (2 w - 3) 3 (3 w - 2) (2 w - 3)$

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7.83

${(2 x + 3)}^{2} {(2 x + 3)}^{2}$

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7.84

${(3 y + 4)}^{2} {(3 y + 4)}^{2}$

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7.85

${(8 y - 5)}^{2} {(8 y - 5)}^{2}$

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7.86

${(4 z - 9)}^{2} {(4 z - 9)}^{2}$

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7.87

${(7 x + 6 y)}^{2} {(7 x + 6 y)}^{2}$

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7.88

${(8 m + 7 n)}^{2} {(8 m + 7 n)}^{2}$

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7.89

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

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7.90

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

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7.91

$2 y {(2 x - 3)}^{2} 2 y {(2 x - 3)}^{2}$

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7.92

$3 q {(3 p + 5)}^{2} 3 q {(3 p + 5)}^{2}$

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7.93

$(h - 9) (h + 9) (h - 9) (h + 9)$

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7.94

$(k - 11) (k + 11) (k - 11) (k + 11)$

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7.95

$(m - 1) (m + 1) (m - 1) (m + 1)$

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7.96

$(9 y - 1) (9 y + 1) (9 y - 1) (9 y + 1)$

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7.97

$(16 m - 5 n) (16 m + 5 n) (16 m - 5 n) (16 m + 5 n)$

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7.98

$(12 p - 3 q) (12 p + 3 q) (12 p - 3 q) (12 p + 3 q)$

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7.99

$(12 - x) (12 + x) (12 - x) (12 + x)$

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7.100

$(13 - p) (13 + p) (13 - p) (13 + p)$

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7.101

$(a^{2} + b^{2}) (a + b) (a - b) (a^{2} + b^{2}) (a + b) (a - b)$

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7.102

$(x^{2} + 4) (x + 2) (x - 2) (x^{2} + 4) (x + 2) (x - 2)$

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7.103

$7 x (y - 5) (y + 5) 7 x (y - 5) (y + 5)$

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7.104

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

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7.105

$8 (a^{2} + 25) 8 (a^{2} + 25)$

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7.106

$9 (4 y^{2} + 9) 9 (4 y^{2} + 9)$

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7.107

$(x + 3) (x^{2} - 3 x + 9) (x + 3) (x^{2} - 3 x + 9)$

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7.108

$(y + 2) (y^{2} - 2 y + 4) (y + 2) (y^{2} - 2 y + 4)$

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7.109

$(u - 5) (u^{2} + 5 u + 25) (u - 5) (u^{2} + 5 u + 25)$

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7.110

$(v - 7) (v^{2} + 7 v + 49) (v - 7) (v^{2} + 7 v + 49)$

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7.111

$(4 - 3 x) (16 + 12 x + 9 x^{2}) (4 - 3 x) (16 + 12 x + 9 x^{2})$

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7.112

$(3 - 2 y) (9 + 6 y + 4 y^{2}) (3 - 2 y) (9 + 6 y + 4 y^{2})$

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7.113

$(2 x - 3 y) (4 x^{2} + 6 x y + 9 y^{2}) (2 x - 3 y) (4 x^{2} + 6 x y + 9 y^{2})$

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7.114

$(10 m - 5 n) (100 m^{2} - 50 m n + 25 n^{2}) (10 m - 5 n) (100 m^{2} - 50 m n + 25 n^{2})$

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7.115

$4 (5 p + q) (25 p^{2} - 5 p q + q^{2}) 4 (5 p + q) (25 p^{2} - 5 p q + q^{2})$

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7.116

$2 (6 c + 7 d) (36 c^{2} - 42 c d + 49 d^{2}) 2 (6 c + 7 d) (36 c^{2} - 42 c d + 49 d^{2})$

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7.117

$3 a^{3} (a + 6) 3 a^{3} (a + 6)$

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7.118

$9 b^{5} (5 b + 3) 9 b^{5} (5 b + 3)$

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7.119

$(5 a - 6) (2 a - 1) (5 a - 6) (2 a - 1)$

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7.120

$(2 x - 3) (4 x - 3) (2 x - 3) (4 x - 3)$

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7.121

$x (x^{2} + 36) x (x^{2} + 36)$

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7.122

$3 (9 y^{2} + 16) 3 (9 y^{2} + 16)$

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7.123

$4 x (2 x - 3) (2 x + 3) 4 x (2 x - 3) (2 x + 3)$

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7.124

$3 (3 y - 4) (3 y + 4) 3 (3 y - 4) (3 y + 4)$

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7.125

${(2 x + 5 y)}^{2} {(2 x + 5 y)}^{2}$

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7.126

${(3 m + 7 n)}^{2} {(3 m + 7 n)}^{2}$

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7.127

$8 (y - 1) (y + 3) 8 (y - 1) (y + 3)$

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7.128

$5 (u - 9) (u + 6) 5 (u - 9) (u + 6)$

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7.129

$2 (5 m + 6) (25 m^{2} - 30 m + 36) 2 (5 m + 6) (25 m^{2} - 30 m + 36)$

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7.130

$3 (3 q + 4) (9 q^{2} - 12 q + 16) 3 (3 q + 4) (9 q^{2} - 12 q + 16)$

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7.131

$4 (a^{2} + 4) (a - 2) (a + 2) 4 (a^{2} + 4) (a - 2) (a + 2)$

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7.132

$7 (y^{2} + 1) (y - 1) (y + 1) 7 (y^{2} + 1) (y - 1) (y + 1)$

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7.133

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

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7.134

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

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7.135

$4 (p - 1) (p - 3) 4 (p - 1) (p - 3)$

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7.136

$3 (q - 2) (2 q + 1) 3 (q - 2) (2 q + 1)$

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7.137

$x = 3, x = −5 x = 3, x = −5$

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7.138

$y = 6, y = −9 y = 6, y = −9$

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7.139

$m = \frac{2}{3}, m = - \frac{1}{2} m = \frac{2}{3}, m = - \frac{1}{2}$

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7.140

$p = - \frac{3}{4}, p = \frac{3}{4} p = - \frac{3}{4}, p = \frac{3}{4}$

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7.141

$u = 0, u = \frac{1}{5} u = 0, u = \frac{1}{5}$

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7.142

$w = 0, w = - \frac{3}{2} w = 0, w = - \frac{3}{2}$

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7.143

$x = 1 x = 1$

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7.144

$v = 2 v = 2$

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7.145

$x = 4, x = −3 x = 4, x = −3$

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7.146

$b = −2, b = −7 b = −2, b = −7$

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7.147

$c = 0, c = \frac{4}{3} c = 0, c = \frac{4}{3}$

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7.148

$d = 3, d = - \frac{1}{2} d = 3, d = - \frac{1}{2}$

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7.149

$a = 0, a = −1 a = 0, a = −1$

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7.150

$b = 0, b = - \frac{1}{3} b = 0, b = - \frac{1}{3}$

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7.151

$p = \frac{7}{5}, p = - \frac{7}{5} p = \frac{7}{5}, p = - \frac{7}{5}$

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7.152

$x = \frac{11}{6}, x = - \frac{11}{6} x = \frac{11}{6}, x = - \frac{11}{6}$

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7.153

$m = 1, m = \frac{3}{2} m = 1, m = \frac{3}{2}$

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7.154

$k = 3, k = −3 k = 3, k = −3$

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7.155

$x = 0, x = \frac{3}{2} x = 0, x = \frac{3}{2}$

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7.156

$y = 0, y = \frac{1}{4} y = 0, y = \frac{1}{4}$

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7.157

$a = - \frac{5}{2}, a = \frac{2}{3} a = - \frac{5}{2}, a = \frac{2}{3}$

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7.158

$b = 2, b = \frac{1}{20} b = 2, b = \frac{1}{20}$

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7.159

$−15, −16 and 15, 16 −15, −16$

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7.160

$−21, −20 and 20, 21 −21, −20$

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7.161

$55$ feet and $66$ feet

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7.162

$1212$ feet and $1515$ feet

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7.163

$55$ feet and $1212$ feet

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7.164

$2424$ feet and $2525$ feet

Section 7.1 Exercises

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$x x$

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$8 w^{2} 8 w^{2}$

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11.

$2 p q 2 p q$

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13.

$6 m^{2} n^{3} 6 m^{2} n^{3}$

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15.

$2 a 2 a$

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17.

$5 x^{3} 5 x^{3}$

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19.

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

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21.

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

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23.

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

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25.

$8 (m - 1) 8 (m - 1)$

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27.

$9 (n - 7) 9 (n - 7)$

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29.

$3 (x^{2} + 2 x - 3) 3 (x^{2} + 2 x - 3)$

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31.

$2 (4 p^{2} + 2 p + 1) 2 (4 p^{2} + 2 p + 1)$

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33.

$8 y^{2} (y + 2) 8 y^{2} (y + 2)$

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35.

$5 x (x^{2} - 3 x + 4) 5 x (x^{2} - 3 x + 4)$

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37.

$6 y^{2} (2 x + 3 x^{2} - 5 y) 6 y^{2} (2 x + 3 x^{2} - 5 y)$

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39.

$−2 (x + 2) −2 (x + 2)$

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41.

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

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43.

$(b - 2) (3 b - 13) (b - 2) (3 b - 13)$

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45.

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

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47.

$(u + 2) (v - 9) (u + 2) (v - 9)$

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49.

$(b - 4) (b + 5) (b - 4) (b + 5)$

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51.

$(p - 9) (p + 4) (p - 9) (p + 4)$

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53.

$−10 (2 x + 1) −10 (2 x + 1)$

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55.

$(x^{2} + 2) (3 x - 7) (x^{2} + 2) (3 x - 7)$

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57.

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

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59.

$w (w - 6) w (w - 6)$

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61.

Answers will vary.

Section 7.2 Exercises

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63.

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

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65.

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

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67.

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

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69.

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

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71.

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

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73.

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

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75.

$(x - 2) (x - 6) (x - 2) (x - 6)$

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77.

$(y - 3) (y - 15) (y - 3) (y - 15)$

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79.

$(x - 1) (x - 7) (x - 1) (x - 7)$

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81.

$(p - 1) (p + 6) (p - 1) (p + 6)$

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83.

$(y + 1) (y - 7) (y + 1) (y - 7)$

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85.

$(x - 4) (x + 3) (x - 4) (x + 3)$

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87.

$(a - 7) (a + 4) (a - 7) (a + 4)$

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89.

$(w - 9) (w + 4) (w - 9) (w + 4)$

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91.

prime

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93.

$(x - 4) (x - 2) (x - 4) (x - 2)$

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95.

$(x - 12) (x + 1) (x - 12) (x + 1)$

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97.

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

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99.

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

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101.

$(m - 2 n) (m - 10 n) (m - 2 n) (m - 10 n)$

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103.

$(x + 8 y) (x - 10 y) (x + 8 y) (x - 10 y)$

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105.

$(m + n) (m - 65 n) (m + n) (m - 65 n)$

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107.

$(a + 8 b) (a - 3 b) (a + 8 b) (a - 3 b)$

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109.

prime

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111.

prime

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113.

$(u - 6) (u - 6) (u - 6) (u - 6)$

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115.

$(x + 2) (x - 16) (x + 2) (x - 16)$

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117.

$(r - 4 s) (r - 16 s) (r - 4 s) (r - 16 s)$

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119.

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

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121.

prime

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123.

$(m + 8 n) (m - 7 n) (m + 8 n) (m - 7 n)$

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125.

$(u - 15 v) (u - 2 v) (u - 15 v) (u - 2 v)$

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127.

prime

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129.

$(x + 8) (x - 7) (x + 8) (x - 7)$

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131.

Answers may vary

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133.

Answers may vary

Section 7.3 Exercises

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135.

ⓐ factor the GCF, binomial ⓑ Undo FOIL ⓒ factor by grouping

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137.

ⓐ undo FOIL ⓑ factor by grouping ⓒ factor the GCF, binomial

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139.

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

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141.

$2 (z - 4) (z + 3) 2 (z - 4) (z + 3)$

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143.

$7 (v - 1) (v - 8) 7 (v - 1) (v - 8)$

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145.

$p (p - 10) (p + 2) p (p - 10) (p + 2)$

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147.

$3 m (m - 5) (m - 2) 3 m (m - 5) (m - 2)$

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149.

$5 x^{2} (x - 3) (x + 5) 5 x^{2} (x - 3) (x + 5)$

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151.

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

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153.

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

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155.

$(4 w - 1) (w - 1) (4 w - 1) (w - 1)$

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157.

$(3 p - 2) (2 p - 5) (3 p - 2) (2 p - 5)$

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159.

$(4 q + 1) (q - 2) (4 q + 1) (q - 2)$

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161.

$(4 p - 3) (p + 5) (4 p - 3) (p + 5)$

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163.

$16 (x - 1) (x - 1) 16 (x - 1) (x - 1)$

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165.

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

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167.

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

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169.

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

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171.

$(2 k - 3) (2 k - 5) (2 k - 3) (2 k - 5)$

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173.

$(5 s - 4) (s - 1) (5 s - 4) (s - 1)$

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175.

$(3 y + 5) (2 y - 3) (3 y + 5) (2 y - 3)$

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177.

$(2 n + 3) (n - 15) (2 n + 3) (n - 15)$

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179.

prime

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181.

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

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183.

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

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185.

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

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187.

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

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189.

$(4 y - 7) (3 y - 2) (4 y - 7) (3 y - 2)$

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191.

$(a - 5) (a + 4) (a - 5) (a + 4)$

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193.

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

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195.

prime

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197.

$13 (z^{2} + 3 z - 2) 13 (z^{2} + 3 z - 2)$

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199.

$(x + 7) (x - 4) (x + 7) (x - 4)$

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201.

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

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203.

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

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205.

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

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207.

$(x + 6) (x - 4) (x + 6) (x - 4)$

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209.

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

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211.

Answers may vary.

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213.

Answers may vary.

Section 7.4 Exercises

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215.

${(4 y + 3)}^{2} {(4 y + 3)}^{2}$

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217.

${(6 s + 7)}^{2} {(6 s + 7)}^{2}$

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219.

${(10 x - 1)}^{2} {(10 x - 1)}^{2}$

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221.

${(5 n - 12)}^{2} {(5 n - 12)}^{2}$

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223.

${(7 x - 2 y)}^{2} {(7 x - 2 y)}^{2}$

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225.

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

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227.

$(8 m - 1)^{2} (8 m - 1)^{2}$

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229.

$10 {(k + 4)}^{2} 10 {(k + 4)}^{2}$

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231.

$3 u {(5 u - v)}^{2} 3 u {(5 u - v)}^{2}$

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233.

$(x - 4) (x + 4) (x - 4) (x + 4)$

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235.

$(5 v - 1) (5 v + 1) (5 v - 1) (5 v + 1)$

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237.

$(11 x - 12 y) (11 x + 12 y) (11 x - 12 y) (11 x + 12 y)$

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239.

$(13 c - 6 d) (13 c + 6 d) (13 c - 6 d) (13 c + 6 d)$

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241.

$(7 x - 2) (7 x + 2) (7 x - 2) (7 x + 2)$ $(2 - 7 x) (2 + 7 x) (2 - 7 x) (2 + 7 x)$

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243.

$(2 z - 1) (2 z + 1) (4 z^{2} + 1) (2 z - 1) (2 z + 1) (4 z^{2} + 1)$

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245.

$5 (q - 3) (q + 3) 5 (q - 3) (q + 3)$

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247.

$6 (4 p^{2} + 9) 6 (4 p^{2} + 9)$

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249.

$(x + 5) (x^{2} - 5 x + 25) (x + 5) (x^{2} - 5 x + 25)$

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251.

$(z - 3) (z^{2} + 3 z + 9) (z - 3) (z^{2} + 3 z + 9)$

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253.

$(2 - 7 t) (4 + 14 t + 49 t^{2}) (2 - 7 t) (4 + 14 t + 49 t^{2})$

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255.

$(2 y - 5 z) (4 y^{2} + 10 y z + 25 z^{2}) (2 y - 5 z) (4 y^{2} + 10 y z + 25 z^{2})$

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257.

$7 (k + 2) (k^{2} - 2 k + 4) 7 (k + 2) (k^{2} - 2 k + 4)$

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259.

$2 (1 - 2 y) (1 + 2 y + 4 y^{2}) 2 (1 - 2 y) (1 + 2 y + 4 y^{2})$

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261.

$(8 a - 5) (8 a + 5) (8 a - 5) (8 a + 5)$

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263.

$3 (3 q - 1) (3 q + 1) 3 (3 q - 1) (3 q + 1)$

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265.

${(4 x - 9)}^{2} {(4 x - 9)}^{2}$

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267.

$2 (4 p^{2} + 1) 2 (4 p^{2} + 1)$

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269.

$(5 - 2 y) (25 + 10 y + 4 y^{2}) (5 - 2 y) (25 + 10 y + 4 y^{2})$

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271.

$5 {(3 n + 2)}^{2} 5 {(3 n + 2)}^{2}$

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273.

${(2 w + 15)}^{2} {(2 w + 15)}^{2}$

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275.

Answers may vary.

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277.

Answers may vary.

Section 7.5 Exercises

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279.

$5 x^{3} (2 x + 7) 5 x^{3} (2 x + 7)$

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281.

$(y - 3) (y + 13) (y - 3) (y + 13)$

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283.

$(2 n - 1) (n + 7) (2 n - 1) (n + 7)$

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285.

$a^{3} (a^{2} + 9) a^{3} (a^{2} + 9)$

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287.

$(11 r - s) (11 r + s) (11 r - s) (11 r + s)$

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289.

$8 (m - 2) (m + 2) 8 (m - 2) (m + 2)$

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291.

${(5 w - 6)}^{2} {(5 w - 6)}^{2}$

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293.

${(m + 7 n)}^{2} {(m + 7 n)}^{2}$

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295.

$7 (b + 3) (b - 2) 7 (b + 3) (b - 2)$

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297.

$3 (x - 3) (x^{2} + 3 x + 9) 3 (x - 3) (x^{2} + 3 x + 9)$

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299.

$(k - 2) (k + 2) (k^{2} + 4) (k - 2) (k + 2) (k^{2} + 4)$

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301.

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

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303.

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

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305.

$u^{2} (u + 1) (u^{2} - u + 1) u^{2} (u + 1) (u^{2} - u + 1)$

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307.

prime

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309.

$10 (m - 5) (m + 5) (m^{2} + 25) 10 (m - 5) (m + 5) (m^{2} + 25)$

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311.

ⓐ $−16 (t^{2} - 5) −16 (t^{2} - 5)$ ⓑ $−8 (2 t + 5) (t - 2) −8 (2 t + 5) (t - 2)$

Section 7.6 Exercises

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315.

$x = 3, x = −7 x = 3, x = −7$

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317.

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

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319.

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

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321.

$y = 3 y = 3$

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323.

$x = 1 / 2 x = 1 / 2$

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325.

$x = −3, x = −4 x = −3, x = −4$

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327.

$a = −4 / 5, a = 6 a = −4 / 5, a = 6$

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329.

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

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331.

$a = −1, a = 0 a = −1, a = 0$

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333.

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

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335.

$y = −1, y = 6 y = −1, y = 6$

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337.

$x = 3 / 2, x = −1 x = 3 / 2, x = −1$

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339.

$p = 0, p = ¾ p = 0, p = ¾$

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341.

$x = 3 / 2 x = 3 / 2$

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343.

$7 and 8; - 8 and −7 7$

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345.

$4 feet and 7 feet 4$

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347.

$6 feet and 8 feet 6$

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349.

$x = −8, x = 3 x = −8, x = 3$

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351.

$p = −1, p = −11 p = −1, p = −11$

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353.

$m = −2, m = 8 m = −2, m = 8$

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355.

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

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357.

$10 and 11; - 11 and −10 10$

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359.

10 feet

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361.

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Review Exercises

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363.

Show solution

365.

$1515$

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367.

$6 (4 x - 7) 6 (4 x - 7)$

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369.

$3 m^{2} (5 m^{2} + 2 n) 3 m^{2} (5 m^{2} + 2 n)$

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371.

$(a + b) (x - y) (a + b) (x - y)$

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373.

$(x - 3) (x + 7) (x - 3) (x + 7)$

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375.

$(m^{2} + 1) (m + 1) (m^{2} + 1) (m + 1)$

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377.

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

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379.

$(k - 6) (k - 10) (k - 6) (k - 10)$

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381.

$(y + 7) (y - 1) (y + 7) (y - 1)$

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383.

$(s - 4) (s + 2) (s - 4) (s + 2)$

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385.

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

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387.

$(a + 7 b) (a - 3 b) (a + 7 b) (a - 3 b)$

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389.

Undo FOIL

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391.

Factor the GCF

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393.

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

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395.

$3 n^{2} (n - 8) (n + 4) 3 n^{2} (n - 8) (n + 4)$

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397.

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

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399.

$(3 a - 1) (6 a - 1) (3 a - 1) (6 a - 1)$

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401.

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

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403.

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

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405.

$3 (x + 4) (x - 3) 3 (x + 4) (x - 3)$

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407.

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

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409.

${(5 x + 3)}^{2} {(5 x + 3)}^{2}$

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411.

${(6 a - 7 b)}^{2} {(6 a - 7 b)}^{2}$

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413.

$10 {(2 x + 9)}^{2} 10 {(2 x + 9)}^{2}$

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415.

$2 y {(y - 4)}^{2} 2 y {(y - 4)}^{2}$

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417.

$(9 r - 5) (9 r + 5) (9 r - 5) (9 r + 5)$

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419.

$(13 m + n) (13 m - n) (13 m + n) (13 m - n)$

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421.

$(5 p - 1) (5 p + 1) (5 p - 1) (5 p + 1)$

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423.

$(3 + 11 y) (3 - 11 y) (3 + 11 y) (3 - 11 y)$

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425.

$5 (2 x - 5) (2 x + 5) 5 (2 x - 5) (2 x + 5)$

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427.

$u (7 u + 3) (7 u - 3) u (7 u + 3) (7 u - 3)$

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429.

$(a - 5) (a^{2} + 5 a + 25) (a - 5) (a^{2} + 5 a + 25)$

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431.

$2 (m + 3) (m^{2} - 3 m + 9) 2 (m + 3) (m^{2} - 3 m + 9)$

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433.

$4 x^{2} (6 x + 11) 4 x^{2} (6 x + 11)$

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435.

${(4 n - 7 m)}^{2} {(4 n - 7 m)}^{2}$

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437.

$(r + 6) (5 r - 8) (r + 6) (5 r - 8)$

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439.

$(n^{2} + 9) (n + 3) (n - 3) (n^{2} + 9) (n + 3) (n - 3)$

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441.

$5 (x - 3) (x + 4) 5 (x - 3) (x + 4)$

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443.

$(m + 5) (m^{2} - 5 m + 25) (m + 5) (m^{2} - 5 m + 25)$

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445.

$a = 3 a = −7 a = 3$

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447.

$m = 0 m = \frac{5}{2} m = –6 m = 0$

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449.

$x = −4, x = −5 x = −4, x = −5$

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451.

$p = - \frac{5}{2}, p = 8 p = - \frac{5}{2}, p = 8$

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453.

$m = \frac{5}{12}, m = - \frac{5}{12} m = \frac{5}{12}, m = - \frac{5}{12}$

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455.

$−21, −22 21, 22 −21, −22$

Practice Test

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457.

$7 (y - 6) 7 (y - 6)$

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459.

$40 a^{2} (2 + 3 a) 40 a^{2} (2 + 3 a)$

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461.

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

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463.

$3 a (a + 4) (a - 6) 3 a (a + 4) (a - 6)$

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465.

$5 (n + 3)^{2} 5 (n + 3)^{2}$

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467.

$(x - 8) (y + 7) (x - 8) (y + 7)$

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469.

${(3 s - 2)}^{2} {(3 s - 2)}^{2}$

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471.

$(10 - a) (10 + a) (10 - a) (10 + a)$

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473.

$3 (x + 5 y) (x - 5 y) 3 (x + 5 y) (x - 5 y)$

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475.

$(a - 3) (b - 2) (a - 3) (b - 2)$

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477.

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

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479.

$y = −11, y = 12 y = −11, y = 12$

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481.

$b = 1, b = −1 b = 1, b = −1$

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483.

$n = - \frac{7}{4}, n = −3 n = - \frac{7}{4}, n = −3$

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485.

$12 and 13; - 13 and −12 12$