A-3 Answers to Selected Exercises 25. -122x 27. 23 m2, or A 23 mB 2 29. 23 12m+ p22, or A 23 2m+ p B 2 31. k2/5 33. -3 # 51/2p3/2 35. 12 37. x 39. 0 x 0 41. 5k20 m0 43. 0 4x - y 0 45. x + 3 47. 14 49. 22 51. x 53. m 55. 242pqr 57. 23 14xy 59. 3 5 61. - 23 5 2 63. 24 m n 65. 23 2 67. 212 2 69. This product cannot be found using the product rule. 71. 622 73. 323 3 75. -224 2 77. -24 79. -15 81. 3223 2 83. 2x2z422x 85. This expression cannot be simplified further. 87. 23 89. 211 91. x323 y 93. 24 5 95. 1222x 97. -11m22 99. 723 3 101. 524 2 103. 723 2 105. -x23 xy2 107. x24 xy 109. 14 + 3xy223 xy2 111. 13x - 2x2224 x2y3 113. This expression cannot be simplified further. 115. 326 + 242 117. 4221 - 8233 119. -7 121. 10 123. 11 + 426 125. 526 127. 5 22 2 129. 23 18 3 131. 24 50 5 133. 26x 3x 135. x2y2xy z 137. 2 23 x2 x2 139. h2 4 9g3hr2 3r2 141. m 23 n2 n 143. x 3 3 2 - 3 3 5 x3 145. 11 22 8 147. - 252 3 9 18 149. -2 + 25 151. -7 + 2 214 + 27 - 222 2 153. 2p - 2 155. 3m A 2 - 2m + nB 4 - m - n 157. 52x A 22x - 2yB 4x - y 159. 17.7 ft per sec 161. -12°F Chapter R Review Exercises 1. 1 25 ; 0.04 3. 3 2 , or 1 1 2 ; 150% 5. 2 3 7. true 9. false 11. true 13. true 15. 52, 6, 9, 106 17. ∅ 19. ∅ 21. 51, 2, 3, 4, 6, 86 23. U, or 51, 2, 3, 4, 5, 6, 7, 8, 9, 106 25. -12, -6, -24 (or -2), 0, 6 27. irrational number, real number 29. whole number, integer, rational number, real number 31. commutative property 33. associative property 35. identity property 37. 29 39. 0 41. 32 43. - 37 18 45. - 12 5 47. -32 49. -13 51. 16 25 53. -10z 8 55. 1 57. -8y11p 59. 1 1p + q25 61. -14r17/12 63. y1/2 65. 1 p2q4 67. 7q3 - 9q2 - 8q + 9 69. 16y3 + 42y2 - 73y + 21 71. 9k2 - 30km+ 25m2 73. -a4 + a - 2 a 75. 6m2 - 3m+ 5 77. 3b - 8 + 2 b2 + 4 79. 31z - 42213z - 112 81. 1z - 8k21z + 2k2 83. 6a614a + 5b212a - 3b2 107. 91x + 2213x2 + 42 109. 2y13x2 + y22 111. prime 113. 4xy 115. k-214k + 12 117. 4t-41t2 + 22 119. z-1/219 + 2z2 121. p-7/41p - 22 123. 4a-7/51-a + 42 125. 1p + 42-3/21p2 + 9p + 212 127. 613x + 12-3/219x2 + 8x + 22 129. 2x12x + 32-5/91-16x4 - 48x3 - 30x2 + 9x + 22 131. In general, a sum of squares is not factorable over the real number system. If there is a greatest common factor, as in 4x2 + 16, it may be factored out, as here, to obtain 41x2 + 42. 133. A7x + 1 5B A7x - 1 5B 135. A5 3 x 2 + 3yB A5 3 x 2 - 3yB 137. {36 139. 9 141. 1x - 121x2 + x + 121x + 121x2 - x + 12 142. 1x - 121x + 121x4 + x2 + 12 143. 1x2 - x + 121x2 + x + 12 144. additive inverse property (0 in the form x2 - x2 was added on the right.); associative property of addition; factoring a perfect square trinomial; factoring a difference of squares; commutative property of addition 145. They are the same. 146. 1x4 - x2 + 121x2 + x + 121x2 - x + 12 R.7 Exercises 1. rational expression 3. 5 5. 4 x 7. 10 x 9. 13x 20 11. 5x x ≠66 13. Ex x ≠- 1 2 , 1F 15. 5x x ≠-2, -3 17. 5x x ≠-16 19. 5x x ≠16 21. 2x + 4 x 23. -3 t + 5 25. 8 9 27. m - 2 m + 3 29. 2m + 3 4m + 3 31. x2 - 4x + 16 33. 2 p 35. 2 9 37. 5x y 39. 2a + 8 a - 3 , or 21a + 42 a - 3 41. 1 43. m + 6 m + 3 45. x 2 - xy + y2 x2 + xy + y2 47. x + 2y 4 - x 49. B, C 51. 19 6k 53. 137 30m 55. a + b a2 57. 5 - 22x 12x2y 59. 3 61. 2x 1x + z21x - z2 63. 4 a - 2 , or -4 2 - a 65. 3x + y 2x - y , or -3x - y y - 2x 67. 4x - 7 x2 - x + 1 69. 2x 2 - 9x 1x - 321x + 421x - 42 71. x + 1 x - 1 73. -1 x + 1 75. 12 - b211 + b2 b11 - b2 77. a + b a2 - ab + b2 79. m3 - 4m - 1 m - 2 81. p3 - 16p + 3 p + 4 83. y2 - 2y - 3 y2 + y - 1 85. -1 x1x + h2 87. -2x - h 1x2 + 9231x + h22 + 94 89. b + a 91. -1 93. y1xy - 92 x2y2 - 9 95. 2x11 - 3x22 1x2 + 125 97. 1 + 2x 3 - 2x 4 99. 3x - 5 12x - 324/3 101. 0 mi 103. 20.1 (thousand dollars) R.8 Exercises 1. 641/3 = 4 3. (a) F (b) H (c) G (d) C 5. t 7. 522 9. -52xy 11. 1251/3 = 5 13. 811/4 = 3 15. 1-12521/3 = -5 17. This expression is not a real number. 19. 321/5 = 2 21. -1-3221/5 = 2 23. 9
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