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Chapter 6

Be Prepared

6.1

11 x 11 x

6.2

3 n + 9 3 n + 9

6.3

a ⋅ a ⋅ a ⋅ a ⋅ a a ⋅ a ⋅ a ⋅ a ⋅ a

6.4

3 4 · 3 4 3 4 · 3 4

6.5

− 8 − 8

6.6

2 x + 6 2 x + 6

6.7

x 2 + 16 x + 63 x 2 + 16 x + 63

6.8

ⓐ 8181 ⓑ 8181 ⓒ −81−81

6.9

1 3 1 3

6.10

32 m 15 32 m 15

6.11

x y x y

6.12

3 + x d 3 + x d

6.13

6 y 2 6 y 2

6.14

11 a 2 + 7 a + 5 11 a 2 + 7 a + 5

6.15

Ten thousands

6.16

Twelve ten thousandths

6.17

8 8

Try It

6.1

ⓐ monomial ⓑ polynomial ⓒ trinomial ⓓ binomial ⓔ monomial

6.2

ⓐ binomial ⓑ trinomial ⓒ monomial ⓓ polynomial ⓔ monomial

6.3

ⓐ 11 ⓑ 44 ⓒ 1212 ⓓ 3 ⓔ 0

6.4

ⓐ 00 ⓑ 55 ⓒ 11 ⓓ 2 ⓔ 3

6.5

21 q 2 21 q 2

6.6

−7 c 2 −7 c 2

6.7

13 m 13 m

6.8

−10 z 3 −10 z 3

6.9

5 y 2 + 3 z 2 5 y 2 + 3 z 2

6.10

−4 m 2 + n 2 −4 m 2 + n 2

6.11

There are no like terms to combine.

6.12

There are no like terms to combine.

6.13

8 x 2 − 11 x + 8 8 x 2 − 11 x + 8

6.14

17 y 2 + 14 y + 1 17 y 2 + 14 y + 1

6.15

x 2 + 3 x − 5 x 2 + 3 x − 5

6.16

6 b 2 + 3 6 b 2 + 3

6.17

2 z 2 + 12 z − 2 2 z 2 + 12 z − 2

6.18

5 x 2 + 14 x + 7 5 x 2 + 14 x + 7

6.19

5 x 2 − 5 x y + 5 y 2 5 x 2 − 5 x y + 5 y 2

6.20

7 x 2 − 6 x y − 2 y 2 7 x 2 − 6 x y − 2 y 2

6.21

− 5 a b + 7 b 2 − 5 a b + 7 b 2

6.22

4 n 2 + 7 m n 4 n 2 + 7 m n

6.23

x 3 − y 3 x 3 − y 3

6.24

p 3 − 2 p 2 q + q 3 p 3 − 2 p 2 q + q 3

6.25

ⓐ 1818 ⓑ 5050 ⓒ −15−15

6.26

ⓐ 1818 ⓑ −4−4 ⓒ 1414

6.27

250 250

6.28

106 106

6.29

$576

6.30

$750

6.31

ⓐ 216 ⓑ 1515 ⓒ 949949 ⓓ 0.1849

6.32

ⓐ 3232 ⓑ 21 ⓒ 81258125 ⓓ 0.0475240.047524

6.33

ⓐ 8181 ⓑ −81−81

6.34

ⓐ 169169 ⓑ −169−169

6.35

b 17 b 17

6.36

x 16 x 16

6.37

ⓐ 5656 ⓑ 418418

6.38

ⓐ 714714 ⓑ 10111011

6.39

ⓐ p6p6 ⓑ y43y43

6.40

ⓐ z8z8 ⓑ b49b49

6.41

x 18 x 18

6.42

b 19 b 19

6.43

ⓐ b35b35 ⓑ 512512

6.44

ⓐ z54z54 ⓑ 349349

6.45

ⓐ 144y2144y2 ⓑ 32w5x532w5x5

6.46

ⓐ 125w3x3125w3x3 ⓑ −27y3−27y3

6.47

ⓐ a48a48 ⓑ −8c12d6−8c12d6

6.48

ⓐ 81x24y2881x24y28 ⓑ q29q29

6.49

ⓐ 75n1275n12 ⓑ 81c24d3081c24d30

6.50

ⓐ 256a22b24256a22b24 ⓑ 40x1040x10

6.51

−35 y 11 −35 y 11

6.52

54 b 9 54 b 9

6.53

6 a 5 b 6 6 a 5 b 6

6.54

8 r 11 s 8 8 r 11 s 8

6.55

5 x + 35 5 x + 35

6.56

3 y + 39 3 y + 39

6.57

x 2 − 7 x x 2 − 7 x

6.58

d 2 − 11 d d 2 − 11 d

6.59

5 x 2 + 20 x y 5 x 2 + 20 x y

6.60

12 p 2 + 2 p r 12 p 2 + 2 p r

6.61

−15 y 3 − 24 y 2 + 21 y −15 y 3 − 24 y 2 + 21 y

6.62

8 x 4 − 12 x 3 + 20 x 2 8 x 4 − 12 x 3 + 20 x 2

6.63

12 x 3 − 20 x 2 + 12 x 12 x 3 − 20 x 2 + 12 x

6.64

−18 a 5 + 12 a 4 − 36 a 3 −18 a 5 + 12 a 4 − 36 a 3

6.65

x p + 8 p x p + 8 p

6.66

a p + 4 p a p + 4 p

6.67

x 2 + 17 x + 72 x 2 + 17 x + 72

6.68

20 x 2 + 51 x + 27 20 x 2 + 51 x + 27

6.69

12 b 2 + 38 b + 30 12 b 2 + 38 b + 30

6.70

a 2 + 17 a + 70 a 2 + 17 a + 70

6.71

30 y 2 − 3 y − 6 30 y 2 − 3 y − 6

6.72

15 c 2 + 14 c − 8 15 c 2 + 14 c − 8

6.73

a 2 − a b + 7 a − 7 b a 2 − a b + 7 a − 7 b

6.74

x 2 − x y + 5 x − 5 y x 2 − x y + 5 x − 5 y

6.75

x 2 + 14 x + 48 x 2 + 14 x + 48

6.76

y 2 + 20 y + 51 y 2 + 20 y + 51

6.77

x 2 − 2 x − 35 x 2 − 2 x − 35

6.78

b 2 + 3 b − 18 b 2 + 3 b − 18

6.79

15 x 2 + 29 x − 14 15 x 2 + 29 x − 14

6.80

16 y 2 − 20 y − 50 16 y 2 − 20 y − 50

6.81

10 c 2 − 60 c − c d + 6 d 10 c 2 − 60 c − c d + 6 d

6.82

14 x 2 − 35 x − 2 x y + 5 y 14 x 2 − 35 x − 2 x y + 5 y

6.83

x 3 − 8 x 2 + 6 x − 48 x 3 − 8 x 2 + 6 x − 48

6.84

y 3 − 9 y 2 + 7 y − 63 y 3 − 9 y 2 + 7 y − 63

6.85

8 a 2 b 2 + 12 a b − 20 8 a 2 b 2 + 12 a b − 20

6.86

8 x 2 y 2 + 2 x y − 15 8 x 2 y 2 + 2 x y − 15

6.87

15 m 2 − 51 m + 42 15 m 2 − 51 m + 42

6.88

42 b 2 − 53 b + 15 42 b 2 − 53 b + 15

6.89

y 3 − 8 y 2 + 17 y − 6 y 3 − 8 y 2 + 17 y − 6

6.90

2 x 3 + 5 x 2 − 7 x + 20 2 x 3 + 5 x 2 − 7 x + 20

6.91

y 3 − 8 y 2 + 17 y − 6 y 3 − 8 y 2 + 17 y − 6

6.92

2 x 3 + 5 x 2 − 7 x + 20 2 x 3 + 5 x 2 − 7 x + 20

6.93

x 2 + 18 x + 81 x 2 + 18 x + 81

6.94

y 2 + 22 y + 121 y 2 + 22 y + 121

6.95

x 2 − 18 x + 81 x 2 − 18 x + 81

6.96

p 2 − 26 p + 169 p 2 − 26 p + 169

6.97

36 x 2 + 36 x + 9 36 x 2 + 36 x + 9

6.98

16 x 2 + 72 x + 81 16 x 2 + 72 x + 81

6.99

4 c 2 − 4 c d + d 2 4 c 2 − 4 c d + d 2

6.100

16 x 2 − 40 x y + 25 y 2 16 x 2 − 40 x y + 25 y 2

6.101

4 x 4 + 4 x 2 + 1 4 x 4 + 4 x 2 + 1

6.102

9 y 6 + 12 y 3 + 4 9 y 6 + 12 y 3 + 4

6.103

x 2 − 25 x 2 − 25

6.104

w 2 − 9 w 2 − 9

6.105

36 x 2 − 25 36 x 2 − 25

6.106

4 x 2 − 49 4 x 2 − 49

6.107

49 − 16 x 2 49 − 16 x 2

6.108

81 − 4 y 2 81 − 4 y 2

6.109

16 p 2 − 49 q 2 16 p 2 − 49 q 2

6.110

9 x 2 − y 2 9 x 2 − y 2

6.111

x 2 y 2 − 36 x 2 y 2 − 36

6.112

a 2 b 2 − 81 a 2 b 2 − 81

6.113

9 x 4 − 16 y 6 9 x 4 − 16 y 6

6.114

4 m 4 − 25 n 6 4 m 4 − 25 n 6

6.115

ⓐ FOIL; 18b2+77b−1818b2+77b−18 ⓑ Binomial Squares; 81p2−72p+1681p2−72p+16 ⓒ Binomial Squares; 49y2+14y+149y2+14y+1 ⓓ Product of Conjugates; 16r2−916r2−9

6.116

ⓐ Binomial Squares; 36x2+84x+4936x2+84x+49 ⓑ Product of Conjugates; 9x2−169x2−16 ⓒ FOIL; 10x2−29x+1010x2−29x+10 ⓓ Binomial Squares; 36n2−12n+136n2−12n+1

6.117

ⓐ x5x5 ⓑ 6969

6.118

ⓐ y6y6 ⓑ 108108

6.119

ⓐ 1x41x4 ⓑ 1121511215

6.120

ⓐ 1m81m8 ⓑ 19111911

6.121

ⓐ b8b8 ⓑ 1z61z6

6.122

ⓐ 1p81p8 ⓑ w4w4

6.123

ⓐ 1 ⓑ 1

6.124

ⓐ 1 ⓑ 1

6.125

ⓐ 11 ⓑ 11

6.126

ⓐ 11 ⓑ 11

6.127

ⓐ 25642564 ⓑ p410,000p410,000 ⓒ m7n7m7n7

6.128

ⓐ 127127 ⓑ −8q3−8q3 ⓒ w4x4w4x4

6.129

m 13 m 13

6.130

k 5 k 5

6.133

r 8 r 8

6.134

v 6 v 6

6.135

a 12 b 8 a 12 b 8

6.136

q 21 r 15 q 21 r 15

6.137

49 x 6 81 y 2 49 x 6 81 y 2

6.138

9 x 8 49 y 2 9 x 8 49 y 2

6.139

1 a 6 1 a 6

6.140

1 p 15 1 p 15

6.141

9 r 18 9 r 18

6.142

2 x 2 x

6.143

7 y 6 7 y 6

6.144

6 z 6 6 z 6

6.145

− 9 a 5 b − 9 a 5 b

6.146

−9 d c 4 −9 d c 4

6.147

2 a 6 3 b 2 2 a 6 3 b 2

6.148

− 3 q 6 5 p 8 − 3 q 6 5 p 8

6.149

4 y 2 7 x 4 4 y 2 7 x 4

6.150

5 8 m 5 n 3 5 8 m 5 n 3

6.151

2 a b 2 2 a b 2

6.152

−4 x y 5 −4 x y 5

6.153

2 z 2 + 6 2 z 2 + 6

6.154

2 z 2 − 3 2 z 2 − 3

6.155

9 b 2 − 11 b 9 b 2 − 11 b

6.156

5 y 2 − 11 y 5 y 2 − 11 y

6.157

−5 y 2 + 3 y −5 y 2 + 3 y

6.158

−7 b 2 + 3 b −7 b 2 + 3 b

6.159

15 d 4 + 6 d 2 15 d 4 + 6 d 2

6.160

36 p 4 − 8 p 2 36 p 4 − 8 p 2

6.161

−4 a + 2 b −4 a + 2 b

6.162

8 a 5 b + 6 a 3 b 2 8 a 5 b + 6 a 3 b 2

6.163

5 x y + 3 y − 2 y 2 5 x y + 3 y − 2 y 2

6.164

5 a 2 + 2 a 2 b − 6 b 2 5 a 2 + 2 a 2 b − 6 b 2

6.165

3 c + 1 − 3 2 c 3 c + 1 − 3 2 c

6.166

2 d − 1 − 2 5 d 2 d − 1 − 2 5 d

6.167

y + 7 y + 7

6.168

m + 5 m + 5

6.169

2 x + 5 2 x + 5

6.170

3 x + 2 3 x + 2

6.171

x 2 + 3 x + 2 + 2 x + 2 x 2 + 3 x + 2 + 2 x + 2

6.172

2 x 2 + 6 x − 5 − 3 x + 1 2 x 2 + 6 x − 5 − 3 x + 1

6.173

x 2 − 2 x + 7 x 2 − 2 x + 7

6.174

x 3 − 8 x 2 + 40 x − 200 x 3 − 8 x 2 + 40 x − 200

6.175

x 2 + 4 x + 16 x 2 + 4 x + 16

6.176

25 x 2 + 10 x + 4 25 x 2 + 10 x + 4

6.177

ⓐ 1818 ⓑ 11071107

6.178

ⓐ 1919 ⓑ 110,000110,000

6.179

ⓐ p8p8 ⓑ 6464

6.180

ⓐ q7q7 ⓑ 1616

6.181

ⓐ 81168116 ⓑ n236m2n236m2

6.182

ⓐ 1252712527 ⓑ 16b4a416b4a4

6.183

ⓐ 125125 ⓑ −125−125 ⓒ 25 ⓓ −25−25

6.184

ⓐ 149149 ⓑ −149−149 ⓒ 49 ⓓ −49−49

6.185

ⓐ 22 ⓑ 118118

6.186

ⓐ 2 ⓑ 12561256

6.187

ⓐ 1y71y7 ⓑ 1z151z15

6.188

ⓐ 1p91p9 ⓑ 1q241q24

6.189

ⓐ 8p8p ⓑ 18p18p ⓒ −18p−18p

6.190

ⓐ 111q111q ⓑ 111q111q−111q−111q ⓒ −11q−11q

6.191

ⓐ x4x4 ⓑ 1y51y5 ⓒ 1z91z9

6.192

ⓐ a5a5 ⓑ 1b41b4 ⓒ 1c151c15

6.193

1 p 3 q 3 1 p 3 q 3

6.194

1 r 2 s 8 1 r 2 s 8

6.195

30 d 3 c 8 30 d 3 c 8

6.196

1 16 x 8 1 16 x 8

6.197

1 16 b 12 1 16 b 12

6.198

64 a 8 64 a 8

6.199

8 c 12 8 c 12

6.200

x 11 x 11

6.201

y 14 y 14

6.202

9.6 × 10 4 9.6 × 10 4

6.203

4.83 × 10 4 4.83 × 10 4

6.204

7.8 × 10 −3 7.8 × 10 −3

6.205

1.29 × 10 −2 1.29 × 10 −2

6.206

1,300

6.207

92,500

6.208

0.00012

6.209

0.075

6.210

0.06

6.211

0.009

6.212

400,000

6.213

20,000

Section 6.1 Exercises

1.

ⓐ trinomial ⓑ polynomial ⓒ binomial ⓓ monomial ⓔ binomial

3.

ⓐ binomial ⓑ trinomial ⓒ polynomial ⓓ trinomial ⓔ monomial

5.

ⓐ 2 ⓑ 4 ⓒ 1 ⓓ 3 ⓔ 0

7.

ⓐ 1 ⓑ 2 ⓒ 3 ⓓ 3 ⓔ 0

9.

12 x 2 12 x 2

11.

6 w 6 w

13.

−5 a −5 a

15.

40 x 40 x

17.

−22 b −22 b

19.

−10a + 5 b −10a + 5 b

21.

−4 a 2 + b 2 −4 a 2 + b 2

23.

x y 2 − 5 x − 5 y 2 x y 2 − 5 x − 5 y 2

25.

a 2 b − 4 a − 5 a b 2 a 2 b − 4 a − 5 a b 2

27.

12a + 8 b 12a + 8 b

29.

−4 a − 3 b −4 a − 3 b

31.

−17 x 6 −17 x 6

33.

11 y 2 + 4 y + 11 11 y 2 + 4 y + 11

35.

−3 x 2 + 17 x − 1 −3 x 2 + 17 x − 1

37.

11 x 2 − 5 x + 5 11 x 2 − 5 x + 5

39.

6 a 2 − 4 a − 1 6 a 2 − 4 a − 1

41.

2 m 2 − 7 m + 4 2 m 2 − 7 m + 4

43.

11 a + 3 11 a + 3

45.

12 s 2 − 16 s + 9 12 s 2 − 16 s + 9

47.

3 x 2 − x + 4 3 x 2 − x + 4

49.

w 2 + 3 w + 4 w 2 + 3 w + 4

51.

2 p 3 + p 2 + 9 p + 10 2 p 3 + p 2 + 9 p + 10

53.

8 a 3 + a 2 − 2 a + 12 8 a 3 + a 2 − 2 a + 12

55.

11 w − 66 11 w − 66

57.

12 c − 45 12 c − 45

59.

10 x 2 − 7 x y + 6 y 2 10 x 2 − 7 x y + 6 y 2

61.

10 m 2 + 3 m n − 8 n 2 10 m 2 + 3 m n − 8 n 2

63.

−3 a b + 3 b 2 −3 a b + 3 b 2

65.

4 u v + 2 v 2 4 u v + 2 v 2

67.

p 3 − 6 p 2 q + p q 2 + 4 q 3 p 3 − 6 p 2 q + p q 2 + 4 q 3

69.

x 3 + 2 x 2 y − 5 x y 2 + y 3 x 3 + 2 x 2 y − 5 x y 2 + y 3

71.

ⓐ 187 ⓑ 40 ⓒ 2

73.

ⓐ −104 ⓑ 4 ⓒ 40

75.

11

77.

$10,800

79.

4

81.

$58

83.

149

85.

Answers will vary.

87.

Answers will vary.

Section 6.2 Exercises

89.

ⓐ 10,000 ⓑ 17 ⓒ 481481 ⓓ 0.125

91.

ⓐ 512 ⓑ 8 ⓒ 27642764
ⓓ 0.064

93.

ⓐ 64 ⓑ −64−64

95.

ⓐ −49−49 ⓑ 4949

97.

ⓐ −0.0001−0.0001 ⓑ 0.0001

99.

x 6 x 6

101.

q 42 q 42

103.

ⓐ 316316 ⓑ 5555

105.

ⓐ w6w6 ⓑ u94u94

107.

y 9 y 9

109.

c 18 c 18

111.

n y + 2 n y + 2

113.

x p + q x p + q

115.

ⓐ b14b14 ⓑ 316316

117.

ⓐ x2yx2y ⓑ 7ab7ab

119.

ⓐ 25x225x2 ⓑ 16a2b216a2b2

121.

ⓐ −343n3−343n3 ⓑ 81x4y4z481x4y4z4

123.

ⓐ w22w22 ⓑ 32x5y2032x5y20

125.

ⓐ −1000q6p12−1000q6p12 ⓑ n40n40

127.

ⓐ 48y448y4 ⓑ 25,000k2425,000k24

129.

ⓐ 432b5432b5 ⓑ 1200j161200j16

131.

ⓐ 128r8128r8 ⓑ 27x2927x29

133.

−18 y 11 −18 y 11

135.

72 u 7 72 u 7

137.

4 f 11 4 f 11

139.

36 a 5 b 7 36 a 5 b 7

141.

8 r 2 s 5 8 r 2 s 5

143.

1 2 x 3 y 3 1 2 x 3 y 3

145.

x 14 x 14

147.

a 36 a 36

149.

8 m 18 8 m 18

151.

1000 x 6 y 3 1000 x 6 y 3

153.

16 a 12 b 8 16 a 12 b 8

155.

8 27 x 6 y 3 8 27 x 6 y 3

157.

1024 a 10 1024 a 10

159.

25000 p 24 25000 p 24

161.

x 18 y 18 x 18 y 18

163.

144 m 8 n 22 144 m 8 n 22

165.

1,000,000 1,000,000

167.

$168.07

169.

Answers will vary.

171.

Answers will vary.

Section 6.3 Exercises

173.

4 w + 40 4 w + 40

175.

−3 a − 21 −3 a − 21

177.

2 x − 14 2 x − 14

179.

−3 k + 12 −3 k + 12

181.

q 2 + 5 q q 2 + 5 q

183.

− b 2 − 9 b − b 2 − 9 b

185.

− x 2 + 10 x − x 2 + 10 x

187.

24 r 2 + 6 r s 24 r 2 + 6 r s

189.

12 x 2 − 120 x 12 x 2 − 120 x

191.

−27 a 2 − 45 a −27 a 2 − 45 a

193.

3 p 2 + 30 p + 75 3 p 2 + 30 p + 75

195.

−8 x 3 − 16 x 2 + 120 x −8 x 3 − 16 x 2 + 120 x

197.

5 q 6 − 10 q 4 + 30 q 3 5 q 6 − 10 q 4 + 30 q 3

199.

−8 y 3 − 16 y 2 + 120 y −8 y 3 − 16 y 2 + 120 y

201.

5 q 5 − 10 q 4 + 30 q 3 5 q 5 − 10 q 4 + 30 q 3

203.

−12 z 4 − 48 z 3 + 4 z 2 −12 z 4 − 48 z 3 + 4 z 2

205.

2 m 2 − 9 m 2 m 2 − 9 m

207.

8 w − 48 8 w − 48

209.

4 x + 40 4 x + 40

211.

15 r − 360 15 r − 360

213.

−3 m − 33 −3 m − 33

215.

−8 z + 40 −8 z + 40

217.

u 2 + 5 u u 2 + 5 u

219.

n 3 − 3 n 2 n 3 − 3 n 2

221.

24 x 2 + 6 x y 24 x 2 + 6 x y

223.

55 p 2 − 25 p q 55 p 2 − 25 p q

225.

3 v 2 + 30 v + 75 3 v 2 + 30 v + 75

227.

8 n 3 − 8 n 2 + 2 n 8 n 3 − 8 n 2 + 2 n

229.

−8 y 3 − 16 y 2 + 120 y −8 y 3 − 16 y 2 + 120 y

231.

5 q 5 − 10 q 4 + 30 q 3 5 q 5 − 10 q 4 + 30 q 3

233.

−12 z 4 − 48 z 3 + 4 z 2 −12 z 4 − 48 z 3 + 4 z 2

235.

2 y 2 − 9 y 2 y 2 − 9 y

237.

w 2 + 12 w + 35 w 2 + 12 w + 35

239.

p 2 + 7 p − 44 p 2 + 7 p − 44

241.

x 2 + 11 x + 24 x 2 + 11 x + 24

243.

y 2 − 8 y + 12 y 2 − 8 y + 12

245.

w 2 + 3 w − 28 w 2 + 3 w − 28

247.

p 2 + 7 p − 60 p 2 + 7 p − 60

249.

6 p 2 + 11 p + 5 6 p 2 + 11 p + 5

251.

20 t 2 − 88 t − 9 20 t 2 − 88 t − 9

253.

15 x 2 − 3 x y − 30 x + 6 y 15 x 2 − 3 x y − 30 x + 6 y

255.

2 a 2 + 5 a b + 3 b 2 2 a 2 + 5 a b + 3 b 2

257.

4 z 2 − 24 z − z y + 6 y 4 z 2 − 24 z − z y + 6 y

259.

x 3 + 2 x 2 + 3 x + 6 x 3 + 2 x 2 + 3 x + 6

261.

x 4 + 3 x 2 − 40 x 4 + 3 x 2 − 40

263.

10 a 2 b 2 + 13 a b − 3 10 a 2 b 2 + 13 a b − 3

265.

24 p 2 q 2 − 42 p q + 15 24 p 2 q 2 − 42 p q + 15

267.

x 3 + 9 x 2 + 23 x + 15 x 3 + 9 x 2 + 23 x + 15

269.

4 y 3 + 33 y 2 + y − 56 4 y 3 + 33 y 2 + y − 56

271.

w 3 − 16 w 2 + 73 w − 70 w 3 − 16 w 2 + 73 w − 70

273.

3 q 3 − 11 q 2 − 19 q − 5 3 q 3 − 11 q 2 − 19 q − 5

275.

14 y − 13 14 y − 13

277.

−11 x − 28 −11 x − 28

279.

15 q 3 − 30 q 2 + 55 q 15 q 3 − 30 q 2 + 55 q

281.

s 2 + 2 s − 63 s 2 + 2 s − 63

283.

y 3 − y 2 − 2 y y 3 − y 2 − 2 y

285.

3 n 3 − n 2 − 25 n + 28 3 n 3 − n 2 − 25 n + 28

287.

49 p 2 − 100 49 p 2 − 100

289.

4 m 4 − 3 m 3 − 7 m 2 4 m 4 − 3 m 3 − 7 m 2

291.

25 a 2 + 70 a b + 49 b 2 25 a 2 + 70 a b + 49 b 2

293.

16 y 2 − 144 z 2 16 y 2 − 144 z 2

295.

ⓐ 306 ⓑ 306 ⓒ Answers will vary.

297.

Answers will vary.

299.

Answers may vary.

301.

Answers may vary.

Section 6.4 Exercises

303.

q 2 + 24 q + 144 q 2 + 24 q + 144

305.

x 2 + 4 3 x + 4 9 x 2 + 4 3 x + 4 9

307.

y 2 − 12 y + 36 y 2 − 12 y + 36

309.

p 2 − 26 p + 169 p 2 − 26 p + 169

311.

16 a 2 + 80 a + 100 16 a 2 + 80 a + 100

313.

9 z 2 + 6 5 z + 1 25 9 z 2 + 6 5 z + 1 25

315.

4 y 2 − 12 y z + 9 z 2 4 y 2 − 12 y z + 9 z 2

317.

1 64 x 2 − 1 36 x y + 1 81 y 2 1 64 x 2 − 1 36 x y + 1 81 y 2

319.

25 u 4 + 90 u 2 + 81 25 u 4 + 90 u 2 + 81

321.

64 p 6 − 48 p 3 + 9 64 p 6 − 48 p 3 + 9

323.

c 2 − 25 c 2 − 25

325.

b 2 − 36 49 b 2 − 36 49

327.

64 j 2 − 16 64 j 2 − 16

329.

81 c 2 − 25 81 c 2 − 25

331.

169 − q 2 169 − q 2

333.

16 − 36 y 2 16 − 36 y 2

335.

49 w 2 − 100 x 2 49 w 2 − 100 x 2

337.

p 2 − 16 25 q 2 p 2 − 16 25 q 2

339.

x 2 y 2 − 81 x 2 y 2 − 81

341.

r 2 s 2 − 4 49 r 2 s 2 − 4 49

343.

36 m 6 − 16 n 10 36 m 6 − 16 n 10

345.

225 m 4 − 64 n 8 225 m 4 − 64 n 8

347.

ⓐ 4r2+48r+1444r2+48r+144 ⓑ 9p2−649p2−64 ⓒ 7a2−48ab−7b27a2−48ab−7b2 ⓓ k2−12k+36k2−12k+36

349.

ⓐ x10−y10x10−y10 ⓑ m6−16m3n+64n2m6−16m3n+64n2 ⓒ 81p2+144pq+64q281p2+144pq+64q2 ⓓ r5+r2s2−r3s3−s5r5+r2s2−r3s3−s5

351.

ⓐ 4,225 ⓑ 4,225 ⓒ Answers will vary.

353.

Answers will vary.

355.

Answers will vary.

Section 6.5 Exercises

357.

ⓐ y10y10 ⓑ 714714

359.

ⓐ u21u21 ⓑ 910910

361.

ⓐ 1t301t30 ⓑ 164164

363.

ⓐ 1x61x6 ⓑ 11001100

365.

ⓐ 1 ⓑ 1

367.

ⓐ −1−1 ⓑ −1−1

369.

ⓐ 1 ⓑ 6

371.

ⓐ 7 ⓑ 1

373.

ⓐ −7−7 ⓑ 0

375.

ⓐ 425425 ⓑ x481x481 ⓒ a5b5a5b5

377.

ⓐ x38y3x38y3 ⓑ 10,00081q410,00081q4

379.

p 7 p 7

381.

x 5 x 5

383.

1

385.

1 n 16 1 n 16

387.

q 18 q 18

389.

1 m 12 1 m 12

391.

a 3 b 18 a 3 b 18

393.

y 20 z 50 y 20 z 50

395.

27 m 15 125 n 3 27 m 15 125 n 3

397.

625 u 28 16 v 12 625 u 28 16 v 12

399.

j 9 j 9

401.

1 q 8 1 q 8

403.

64 k 6 64 k 6

405.

−4,000 −4,000

407.

7 v 8 7 v 8

409.

−6 u 8 −6 u 8

411.

− 3 x 3 y 12 − 3 x 3 y 12

413.

2 m 3 3 n 5 2 m 3 3 n 5

415.

−3 y 3 4 x 3 −3 y 3 4 x 3

417.

65 a 3 b 2 42 c 3 65 a 3 b 2 42 c 3

419.

−3 q 5 p 5 −3 q 5 p 5

421.

5 v 4 u 2 5 v 4 u 2

423.

ⓐ 18n1018n10 ⓑ 12n1012n10 ⓒ 45n2045n20 ⓓ 5

425.

ⓐ q8q8 ⓑ q15q15

427.

ⓐ zz ⓑ 1z1z

429.

6 y 6 6 y 6

431.

15 c 6 15 c 6

433.

3 x 2 3 x 2

435.

− y z 2 − y z 2

437.

10 3 10 3

439.

Answers will vary.

441.

Answers will vary.

Section 6.6 Exercises

443.

6 b + 15 6 b + 15

445.

6 x 2 − 2 x 6 x 2 − 2 x

447.

11 w − 2 11 w − 2

449.

4 x 2 + 3 x 4 x 2 + 3 x

451.

−5 b 2 + 3 b −5 b 2 + 3 b

453.

−17 m 4 − 24 m 3 −17 m 4 − 24 m 3

455.

103 z 5 − 12 z 2 103 z 5 − 12 z 2

457.

17 y 2 + 14 17 y 2 + 14

459.

−5 x 3 + 3 −5 x 3 + 3

461.

−6 y 2 + 3 y −6 y 2 + 3 y

463.

9 x 2 y 3 + 12 y 9 x 2 y 3 + 12 y

465.

7 c − 10 c 2 d − 5 c d 2 7 c − 10 c 2 d − 5 c d 2

467.

6 r 3 + 11 r 2 s − 8 r s 3 6 r 3 + 11 r 2 s − 8 r s 3

469.

4 q + 1 − 1 3 q 4 q + 1 − 1 3 q

471.

−5 y − 3 + 1 4 y −5 y − 3 + 1 4 y

473.

7 a − 12 + 11 a 7 a − 12 + 11 a

475.

d + 6 d + 6

477.

a − 7 a − 7

479.

x − 7 x − 7

481.

4 x + 3 4 x + 3

483.

p + 3 − 8 p + 8 p + 3 − 8 p + 8

485.

x + 7 + 5 x − 5 x + 7 + 5 x − 5

487.

2 n 2 − 6 n + 8 2 n 2 − 6 n + 8

489.

7 q 2 + 7 q + 2 7 q 2 + 7 q + 2

491.

m 2 − 10 m + 100 m 2 − 10 m + 100

493.

x 2 + 6 x + 36 x 2 + 6 x + 36

495.

25 y 2 + 20 x + 16 25 y 2 + 20 x + 16

497.

45

499.

Answers will vary.

Section 6.7 Exercises

501.

ⓐ 181181 ⓑ 11001100

503.

ⓐ 12561256 ⓑ 11001100

505.

ⓐ c5c5 ⓑ 25

507.

ⓐ t9t9 ⓑ 10000

509.

ⓐ 10091009 ⓑ −c3d38−c3d38

511.

ⓐ 83438343 ⓑ −x3y627−x3y627

513.

ⓐ 149149 ⓑ −149−149 ⓒ 49 ⓓ −49−49

515.

ⓐ −1125−1125 ⓑ −125−125 ⓒ −125−125 ⓓ −1125−1125

517.

ⓐ 2525 ⓑ 110110

519.

ⓐ 316316 ⓑ 11441144

521.

ⓐ 1b51b5 ⓑ 1k101k10

523.

ⓐ 1s81s8 ⓑ 1a901a90

525.

ⓐ 6r6r ⓑ 16r16r ⓒ −16r−16r

527.

ⓐ 116q4116q4 ⓑ 2q42q4 ⓒ −2q4−2q4

529.

ⓐ 1s41s4 ⓑ 1q51q5 ⓒ 1y71y7

531.

ⓐ 1 ⓑ y6y6 ⓒ 1y41y4

533.

1 x 1 x

535.

1 m 2 n 4 1 m 2 n 4

537.

1 p 5 q 7 1 p 5 q 7

539.

− 14 k 5 j 3 − 14 k 5 j 3

541.

− 40 n 3 m − 40 n 3 m

543.

1 64 y 9 1 64 y 9

545.

4 p 10 4 p 10

547.

n 7 n 7

549.

y 5 y 5

551.

3.4 × 10 5 3.4 × 10 5

553.

1.29 × 10 6 1.29 × 10 6

555.

4.1 × 10 −2 4.1 × 10 −2

557.

1.03 × 10 −6 1.03 × 10 −6

559.

830

561.

16,000,000,000

563.

0.038

565.

0.0000193

567.

0.02

569.

0.0000056 0.0000056

571.

500,000,000

573.

20,000,000

575.

6.85×1096.85×109.

577.

5.7 × 10 −9 5.7 × 10 −9

579.

15,000,000,000,000

581.

0.00001

583.

1.545 × 10 8 1.545 × 10 8

585.

ⓐ 1.86×10131.86×1013 ⓑ 3×1083×108 ⓒ 6.2×1046.2×104

587.

answers will vary

Review Exercises

589.

ⓐ binomial ⓑ monomial ⓒ trinomial ⓓ trinomial ⓔ other polynomial

591.

ⓐ 3 ⓑ 4 ⓒ 2 ⓓ 4 ⓔ 0

593.

5 k 5 k

595.

−27 c −27 c

597.

7 n 2 7 n 2

599.

13a + b 13a + b

601.

13 p 2 − 5 p − 1 13 p 2 − 5 p − 1

603.

7 y 2 − 9 y + 4 7 y 2 − 9 y + 4

605.

5 a 3 + a 2 + 6 a + 2 5 a 3 + a 2 + 6 a + 2

607.

ⓐ −26−26 ⓑ 10 ⓒ 22

609.

12,000

611.

17

613.

0.125

615.

−64 −64

617.

p 31 p 31

619.

8 6 8 6

621.

y c + 3 y c + 3

623.

5 6 5 6

625.

3 r s 3 r s

627.

−125 y 3 −125 y 3

629.

1000 x 3 y 3 z 3 1000 x 3 y 3 z 3

631.

64 a 9 b 6 64 a 9 b 6

633.

144 q 14 144 q 14

635.

8 125 m 6 n 3 8 125 m 6 n 3

637.

144 n 8 144 n 8

639.

15 a 2 b 5 15 a 2 b 5

641.

−4 y − 52 −4 y − 52

643.

p 2 + 3 p p 2 + 3 p

645.

−12 u 2 − 42 u −12 u 2 − 42 u

647.

9 q 4 − 63 q 3 + 54 q 2 9 q 4 − 63 q 3 + 54 q 2

649.

11 b − 44 11 b − 44

651.

ⓐ 12y2−44y+3512y2−44y+35 ⓑ 12y2−44y+3512y2−44y+35 ⓒ 12y2−44y+3512y2−44y+35

653.

y 2 − 12 y + 32 y 2 − 12 y + 32

655.

q 2 + 13 q − 48 q 2 + 13 q − 48

657.

u 4 + u 2 − 30 u 4 + u 2 − 30

659.

16 m 2 n 2 − 2 m n − 3 16 m 2 n 2 − 2 m n − 3

661.

ⓐ 18x3−21x2−34x+4018x3−21x2−34x+40 ⓑ 18x3−21x2−34x+4018x3−21x2−34x+40

663.

7 m 3 − 69 m 2 − 31 m − 3 7 m 3 − 69 m 2 − 31 m − 3

665.

q 2 − 30 q + 225 q 2 − 30 q + 225

667.

64 u 2 + 16 u + 1 64 u 2 + 16 u + 1

669.

16 a 2 − 24 a b + 9 b 2 16 a 2 − 24 a b + 9 b 2

671.

y 2 − 4 25 y 2 − 4 25

673.

36 − r 2 36 − r 2

675.

25 p 8 − 16 q 6 25 p 8 − 16 q 6

677.

36 a 2 − 121 36 a 2 − 121

679.

c 8 + 18 c 4 d + 81 d 2 c 8 + 18 c 4 d + 81 d 2

681.

4 a 3 − a 2 b 2 + 16 a b − 4 b 3 4 a 3 − a 2 b 2 + 16 a b − 4 b 3

683.

10 20 10 20

685.

1 v 36 1 v 36

687.

1 5 7 1 5 7

689.

1

691.

−1

693.

1

695.

0

697.

m 4 81 m 4 81

699.

x 6 64 y 6 x 6 64 y 6

701.

1

703.

r 20 r 20

705.

243 x 20 32 y 10 243 x 20 32 y 10

707.

− 10,125 n 10 4 − 10,125 n 10 4

709.

− 4 b 6 a 5 − 4 b 6 a 5

711.

9 p 2 9 p 2

713.

7 x − 15 7 x − 15

715.

55 p 3 − 30 p 55 p 3 − 30 p

717.

12 a 4 − 6 a 3 b − 7 a b 2 12 a 4 − 6 a 3 b − 7 a b 2

719.

21 y 2 + 10 − 1 y 2 21 y 2 + 10 − 1 y 2

721.

v − 8 v − 8

723.

n − 6 + 4 n + 3 n − 6 + 4 n + 3

725.

u 2 + 2 u + 4 u 2 + 2 u + 4

727.

− 1 125 − 1 125

729.

1 216 u 3 1 216 u 3

731.

16 9 16 9

733.

1 q 11 1 q 11

735.

1 y 8 1 y 8

737.

1 a 4 1 a 4

739.

r r

741.

4.29 × 10 −3 4.29 × 10 −3

743.

7.2 × 10 9 7.2 × 10 9

745.

15,000,000,000 15,000,000,000

747.

0.55 0.55

749.

0.0217 0.0217

751.

0.0000003 0.0000003

Practice Test

753.

15 a 2 + a − 6 15 a 2 + a − 6

755.

− 8 125 − 8 125

757.

16 a 6 b 10 16 a 6 b 10

759.

3 k 3 − 21 k 2 + 39 k 3 k 3 − 21 k 2 + 39 k

761.

9 v 2 − 86 v + 45 9 v 2 − 86 v + 45

763.

n 3 − 11 n 2 + 34 n − 24 n 3 − 11 n 2 + 34 n − 24

765.

49 p 2 − 25 49 p 2 − 25

767.

1 9 1 9

769.

1 1

771.

6 x + 21 − 3 x 6 x + 21 − 3 x

773.

16 x 2 + 4 x + 1 16 x 2 + 4 x + 1

775.

1 25 1 25

777.

1 q 9 1 q 9

779.

8.3 × 10 7 8.3 × 10 7

781.

74,800

783.

424 feet

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