80 CHAPTER R Review of Basic Concepts 24. -814 - y2 1y + 221y - 42 25. 8k + 16 9k + 18 26. 20r + 10 30r + 15 27. m2 - 4m+ 4 m2 + m- 6 28. r2 - r - 6 r2 + r - 12 29. 8m2 + 6m- 9 16m2 - 9 30. 6y2 + 11y + 4 3y2 + 7y + 4 31. x3 + 64 x + 4 32. y3 - 27 y - 3 Multiply or divide, as indicated. See Example 3. 33. 15p3 9p2 # 12p 10p3 34. 8r3 6r # 5r2 9r3 35. 2k + 8 6 , 3k + 12 2 36. 5m+ 25 10 , 6m+ 30 12 37. x2 + x 5 # 25 xy + y 38. y3 + y2 7 # 49 y4 + y3 39. 4a + 12 2a - 10 , a2 - 9 a2 - a - 20 40. 6r - 18 9r2 + 6r - 24 , 4r - 12 12r - 16 41. p2 - p - 12 p2 - 2p - 15 # p2 - 9p + 20 p2 - 8p + 16 42. x2 + 2x - 15 x2 + 11x + 30 # x2 + 2x - 24 x2 - 8x + 15 43. m2 + 3m+ 2 m2 + 5m+ 4 , m2 + 5m+ 6 m2 + 10m+ 24 44. y2 + y - 2 y2 + 3y - 4 , y2 + 3y + 2 y2 + 4y + 3 45. x3 + y3 x3 - y3 # x2 - y2 x2 + 2xy + y2 46. x2 - y2 1x - y22 # x2 - xy + y2 x2 - 2xy + y2 , x3 + y3 1x - y24 47. xz - xw + 2yz - 2yw z2 - w2 # 4z + 4w + xz + wx 16 - x2 48. ac + ad + bc + bd a2 - b2 # a3 - b3 2a2 + 2ab + 2b2 49. Concept Check Which of the following rational expressions is equivalent to -1? In choices A, B, and D, x ≠-4, and in choice C, x ≠4. (Hint: There may be more than one answer.) A. x - 4 x + 4 B. -x - 4 x + 4 C. x - 4 4 - x D. x - 4 -x - 4 50. Explain how to find the least common denominator of several fractions. Add or subtract, as indicated. See Example 4. 51. 3 2k + 5 3k 52. 8 5p + 3 4p 53. 1 6m + 2 5m + 4 m 54. 8 3p + 5 4p + 9 2p 55. 1 a + b a2 56. 3 z + x z2 57. 5 12x2y - 11 6xy 58. 7 18a3b2 - 2 9ab 59. 17y + 3 9y + 7 - -10y - 18 9y + 7 60. 7x + 8 3x + 2 - x + 4 3x + 2 61. 1 x + z + 1 x - z 62. m+ 1 m- 1 + m- 1 m+ 1 63. 3 a - 2 - 1 2 - a 64. 4 p - q - 2 q - p 65. x + y 2x - y - 2x y - 2x 66. m- 4 3m- 4 - 5m 4 - 3m
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