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Prealgebra 2e

Chapter 10

Prealgebra 2eChapter 10
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  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

Be Prepared

10.1

11x11x

10.2

3n+93n+9

10.3

100100

10.4

916916

10.5

88

10.6

2x+62x+6

10.7

44+33a44+33a

10.8

x2+16x+63x2+16x+63

10.9

1313

10.10

32m1532m15

10.11

xyxy

10.12

ten thousand

10.13

twelve ten-thousandths

10.14

88

10.15

22272227

10.16

18a3318a33

10.17

4x4+12x34x24x4+12x34x2

Try It

10.1
  1. monomial
  2. polynomial
  3. trinomial
  4. binomial
  5. monomial
10.2
  1. binomial
  2. trinomial
  3. polynomial
  4. monomial
  5. monomial
10.3
  1. 1
  2. 1
  3. 4
  4. 2
  5. 0
10.4
  1. 0
  2. 2
  3. 4
  4. 5
  5. 3
10.5

17x2

10.6

−3y2

10.7

14n

10.8

−2a3

10.9

−2x2 + 3y2

10.10

−2a2 + b2

10.11

4x2 − 8x + 10

10.12

11y2 + 9y − 5

10.13

3y2 + 3y + 3

10.14

3u2u + 2

10.15

4n2 + 12n

10.16

5a2 + 8a + 8

10.17
  1. 13
  2. 3
10.18
  1. 114
  2. −2
10.19

4 feet

10.20

20 feet

10.21
  1. 64
  2. 11
10.22
  1. 81
  2. 21
10.23
  1. 25642564
  2. 0.44890.4489
10.24
  1. 81258125
  2. 0.0161290.016129
10.25
  1. 16
  2. −16
10.26
  1. 64
  2. −64
10.27

x15

10.28

x16

10.29

p10

10.30

m8

10.31

610

10.32

915

10.33

y43

10.34

z39

10.35

x21

10.36

y15

10.37
  1. x28
  2. 732
10.38
  1. x54
  2. 842
10.39

196x2

10.40

144a2

10.41

256x4y4

10.42

216x3y3

10.43

x40

10.44

y42

10.45

−512x12y21

10.46

81a20b24

10.47

98n14

10.48

48m5

10.49

64u18v22

10.50

675x7y18

10.51

−56x11

10.52

54y9

10.53

12m5n6

10.54

12p11q8

10.55

6x + 48

10.56

2y + 24

10.57

y2 − 9y

10.58

p2 − 13p

10.59

8x2 + 24xy

10.60

18r2 + 3rs

10.61

−32y3 − 20y2 + 36y

10.62

−54x3 − 6x2 + 6x

10.63

12x4 − 9x3 + 27x2

10.64

24y4 − 16y3 − 32y2

10.65

xp + 8p

10.66

ap + 4p

10.67

x2 + 17x + 72

10.68

a2 + 9a + 20

10.69

20x2 + 51x + 27

10.70

80m2 + 142m + 63

10.71

56y2 − 13y − 3

10.72

15x2 − 14x − 16

10.73

x2xy + 5x − 5y

10.74

x2x + 2xy − 2y

10.75

x2 + 15x + 56

10.76

y2 + 16y + 28

10.77

y2 + 5y − 24

10.78

q2 + q − 20

10.79

20a2 + 37a − 18

10.80

49x2 − 28x − 32

10.81

12x2 − 60xxy + 5y

10.82

12a2 − 54a − 2ab + 9b

10.83

12m2 − 55m + 63

10.84

42n2 − 47n + 10

10.85

y3 − 8y2 + 9y − 2

10.86

3x3 + 2x2 − 3x + 10

10.87

y3 − 8y2 + 9y − 2

10.88

3x3 + 2x2 − 3x + 10

10.89
  1. x3
  2. 79
10.90
  1. y6
  2. 88
10.91
  1. 1x71x7
  2. 1121011210
10.92
  1. 1m91m9
  2. 176176
10.93
  1. b8b8
  2. 1z61z6
10.94
  1. 1p81p8
  2. w4w4
10.95
  1. 1
  2. 1
10.96
  1. 1
  2. 1
10.97

1

10.98

1

10.99
  1. 1
  2. 7x2
10.100
  1. −23x2
  2. 1
10.101
  1. 49814981
  2. y3512y3512
  3. p6q6p6q6
10.102
  1. 164164
  2. 125m3125m3
  3. r4s4r4s4
10.103

a11

10.104

b19

10.105

k2

10.106

1d1d

10.107

f12

10.108

1b101b10

10.109

m15n40m15n40

10.110

t20u14t20u14

10.111

25b281c625b281c6

10.112

64p12343q1564p12343q15

10.113

1y111y11

10.114

9x5

10.115

7x4

10.116

16y3

10.117

12yx212yx2

10.118

9a59a5

10.119

2a63b22a63b2

10.120

3q65p83q65p8

10.121

4y27x44y27x4

10.122

58m5n358m5n3

10.123

2xy2

10.124

−4ab5

10.125
  1. 1818
  2. 11001100
10.126
  1. 1919
  2. 110,000110,000
10.127
  1. 125125
  2. 125125
10.128
  1. 1414
  2. 1414
10.129
  1. 22
  2. 118118
10.130
  1. 22
  2. 12561256
10.131

1y71y7

10.132

1z81z8

10.133
  1. 8p8p
  2. 18p18p
  3. 18p18p
10.134
  1. 11q11q
  2. 111q111q
  3. 111q111q
10.135
  1. x4x4
  2. 1y51y5
  3. 1z91z9
10.136
  1. a5a5
  2. 1b41b4
  3. 1c151c15
10.137

1p3q31p3q3

10.138

1r2s81r2s8

10.139

12v5u12v5u

10.140

30d3c830d3c8

10.141

1x41x4

10.142

1y41y4

10.143

64a864a8

10.144

8c128c12

10.145

x11

10.146

y13

10.147

9.6 × 104

10.148

4.83 × 104

10.149

7.8 × 10−3

10.150

1.29 × 10−2

10.151

1,300

10.152

92,500

10.153

0.00012

10.154

0.075

10.155

0.06

10.156

0.009

10.157

400,000

10.158

20,000

10.159

18

10.160

16

10.161

7

10.162

11

10.163

8x2

10.164

9y3

10.165

3x

10.166

5m2

10.167

4(x + 3)

10.168

6(a + 4)

10.169

9(a + 1)

10.170

11(x + 1)

10.171

11(x − 4)

10.172

13(y − 4)

10.173

4(y2 + 2y + 3)

10.174

6(x2 + 7x − 2)

10.175

x(9x + 7)

10.176

a(5a − 12)

10.177

2x2(x + 6)

10.178

3y2(2y − 5)

10.179

9y(2y + 7)

10.180

8k(4k + 7)

10.181

6y(3y2y − 4)

10.182

4x(4x2 + 2x − 3)

10.183

−5(y + 7)

10.184

−8(2z + 7)

10.185

−7a(a − 3)

10.186

x(6x − 1)

Section 10.1 Exercises

1.

binomial

3.

trinomial

5.

polynomial

7.

monomial

9.

5

11.

1

13.

0

15.

15x2

17.

−8u

19.

5a + 7b

21.

−4a −3b

23.

16x

25.

−17x6

27.

12y2 + 4y + 8

29.

−3x2 + 17x − 1

31.

4a2 − 7a − 11

33.

4m2 − 10m + 2

35.

11z + 8

37.

12s2 − 16s + 9

39.

2p3 + p2 + 9p + 10

41.

x2 + 3x + 4

43.

11w − 66

45.
  1. 187
  2. 40
  3. 2
47.
  1. −104
  2. 4
  3. 40
49.

19 feet

51.

10 mpg

53.

Answers will vary.

Section 10.2 Exercises

55.

1,024

57.

1414

59.

0.008

61.

625

63.

−625

65.

−10,000

67.

827827

69.

−0.25

71.

x9

73.

a5

75.

314

77.

z6

79.

xa+2

81.

ya+b

83.

u8

85.

y20

87.

1012

89.

x90

91.

x2y

93.

5xy

95.

25a2

97.

−216m3

99.

16r2s2

101.

256x4y4z4

103.

x14

105.

a36

107.

45x3

109.

200a5

111.

8m18

113.

1,000x6y3

115.

16a12b8

117.

827x6y3827x6y3

119.

1,024a10

121.

25,000p24

123.

x18y18

125.

144m8n22

127.

−60x6

129.

72u7

131.

4r11

133.

36a5b7

135.

8x2y5

137.

12x3y312x3y3

139.

1,679,616

141.

Answers will vary.

143.

Answers will vary.

Section 10.3 Exercises

145.

4x + 40

147.

15r − 360

149.

−3m − 33

151.

−8z + 40

153.

u2 + 5u

155.

n3 − 3n2

157.

12x2 − 120x

159.

−27a2 − 45a

161.

24x2 + 6xy

163.

55p2 − 25pq

165.

3v2 + 30v + 75

167.

8n3 − 8n2 + 2n

169.

−8y3 − 16y2 + 120y

171.

5q5 − 10q4 + 30q3

173.

−12z4 − 48z3 + 4z2

175.

2y2 − 9y

177.

8w − 48

179.

x2 + 10x + 24

181.

n2 + 9n − 36

183.

y2 + 11y + 24

185.

a2 + 22a + 96

187.

u2 − 14u + 45

189.

z2 − 32z + 220

191.

x2 + 3x − 28

193.

v2 + 7v − 60

195.

6n2 + 11n + 5

197.

20m2 − 88m − 9

199.

16c2 − 1

201.

15u2 − 82u + 112

203.

2a2 + 5ab + 3b2

205.

5x2 − 20xxy + 4y

207.

u3 + 7u2 + 14u + 8

209.

3a3 + 31a2 + 5a − 50

211.

y3 − 16y2 + 69y − 54

213.

2x3 − 9x2 − 17x − 6

215.
  1. 195
  2. 195
  3. Answers will vary.
217.

Answers will vary.

Section 10.4 Exercises

219.

46

221.

x9

223.

r4

225.

1y161y16

227.

1101211012

229.

1a81a8

231.

1

233.

1

235.

−1

237.
  1. 1
  2. 10
239.
  1. 1
  2. −27x5
241.
  1. 1
  2. 15
243.

7

245.

2433224332

247.

m3216m3216

249.

x10y10x10y10

251.

a29b2a29b2

253.

x3

255.

u2

257.

1y21y2

259.

1

261.

1x181x18

263.

a14

265.

y3

267.

1x101x10

269.

16r12625s416r12625s4

271.

1

273.

1r31r3

275.

3x8

277.

8b6

279.

−18x6−18x6

281.

2x

283.

56x656x6

285.

6r2s86r2s8

287.

n68n68

289.

4y65x24y65x2

291.

4z3x2y34z3x2y3

293.

10n2m410n2m4

295.

5u4v3

297.
  1. 18n1018n10
  2. 12n1012n10
  3. 45n2045n20
  4. 55
299.
  1. q8q8
  2. q15q15
301.
  1. zz
  2. 1z1z
303.

6y66y6

305.

15c615c6

307.

3x23x2

309.

yz2yz2

311.

1,000,000

313.

Answers will vary.

315.

Answers will vary.

Section 10.5 Exercises

317.

164164

319.

132132

321.

110110

323.

4949

325.

3535

327.

3434

329.
  1. 164164
  2. 164164
331.
  1. 1409614096
  2. 1409614096
333.
  1. 103103
  2. 130130
335.
  1. 325325
  2. 12251225
337.

1p31p3

339.

1m51m5

341.
  1. 3q3q
  2. 13q13q
  3. 13q13q
343.
  1. 10k10k
  2. 110k110k
  3. 110k110k
345.

r3

347.

1q51q5

349.

1z81z8

351.

1m1m

353.

1x1x

355.

u2v2u2v2

357.

1a2b41a2b4

359.

1p5q71p5q7

361.

21q5p321q5p3

363.

32a3b32a3b

365.

1q1001q100

367.

1x41x4

369.

1p61p6

371.

m6

373.

9q109q10

375.

n1864n1864

377.

b8

379.

m7

381.

1r31r3

383.

p3

385.

2.8 × 105

387.

1.29 × 106

389.

4.1 × 10−2

391.

1.03 × 10−5

393.

6.85 × 109

395.

5.7 × 10−9

397.

830

399.

16,000,000,000

401.

0.028

403.

0.0000000615

405.

$15,000,000,000,000

407.

0.00001

409.

0.003

411.

0.00000735

413.

20,000,000

415.

50,000,000

417.
  1. 1.25 × 10−4
  2. 8,000
419.

11,441,304,000

421.

Answers will vary.

Section 10.6 Exercises

423.

15

425.

25

427.

4

429.

5

431.

3x

433.

12p3

435.

2a

437.

10y

439.

5x3

441.

7b2

443.

5(y + 3)

445.

4(b − 5)

447.

7(x − 1)

449.

3(n2 + 7n + 4)

451.

6(q2 + 5q + 7)

453.

c(9c + 22)

455.

x(17x + 7)

457.

q(4q + 7)

459.

3r(r + 9)

461.

10u(3u − 1)

463.

b(a + 8)

465.

11y(5 − y3)

467.

15c2(3c − 1)

469.

6c(c2d2)

471.

24x2(2x + 3)

473.

18a3(8a3 + 5)

475.

10(y2 + 5y + 4)

477.

12(u2 − 3u − 9)

479.

5p2(p2 − 4p − 3)

481.

8c3(c2 + 5c − 7)

483.

−7(p + 12)

485.

−6b(3b + 11)

487.

−8a2(a − 4)

489.

−9b3(b2 − 7)

491.

−4(4t2 − 20t − 1)

493.

Answers will vary.

Review Exercises

494.

trinomial

496.

binomial

498.

2

500.

0

502.

15p

504.

−3n5

506.

10a2 + 4a − 1

508.

6y2 − 3y + 3

510.

8q3 + q2 + 6q − 29

512.

995

514.

2,955

516.

−163

518.

64 feet

520.

216

522.

0.25

524.

p13

526.

a6

528.

y12

530.

310

532.

64n2

534.

256a8b8

536.

27a15

538.

x21

540.

−54p5

542.

56x3y11

544.

70 − 7x

546.

−625y4 + 5y

548.

a2 + 7a + 10

550.

6x2 − 19x − 7

552.

n2 + 9n + 8

554.

5u2 + 37u − 24

556.

p2 + 11p + 28

558.

27c2 − 3c − 4

560.

x3 − 2x2 − 24x − 21

562.

m3m2 − 72m − 180

564.

26 or 64

566.

1n91n9

568.

1

570.

1

572.

925925

574.

125m3n3125m3n3

576.

a2

578.

1x401x40

580.

1n1n

582.

9p9

584.

3y43y4

586.

4a5b24a5b2

588.

4m9n44m9n4

590.

136136

592.

516516

594.

x6

596.

1u3v51u3v5

598.

k6

600.

b10

602.

5.3 × 106

604.

9.7 × 10−2 millimeter

606.

29,000

608.

0.375

610.

6,000

612.

30,000,000,000

614.

5

616.

4x2

618.

8(2u − 3)

620.

6p(p + 1)

622.

−9a3(a2 + 1)

624.

5(y2 − 11y + 9)

Practice Test

626.
  1. trinomial
  2. 4
628.

6x2 − 3x + 11

630.

n5

632.

−48x5y9

634.

s2 + 17s + 72

636.

55a2 − 41a + 6

638.

24a2 + 34ab − 45b2

640.

x14

642.

4rs64rs6

644.

3y2 − 7x

646.

18y318y3

648.

x9

650.

−6x(x + 5)

652.

0.000525

654.

3 × 105

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