102 CHAPTER R Review of Basic Concepts Factor as completely as possible. 79. 31z - 422 + 91z - 423 80. 7z2 - 9z3 + z 81. z2 - 6zk - 16k2 82. r2 + rp - 42p2 83. 48a8 - 12a7b - 90a6b2 84. 6m2 - 13m- 5 85. 49m8 - 9n2 86. 169y4 - 1 87. 613r - 122 + 13r - 12 - 35 88. 8y3 - 1000z6 89. xy + 2x - y - 2 90. 15mp + 9mq - 10np - 6nq Factor each expression. (These expressions arise in calculus from a technique called the product rule that is used to determine the shape of a curve.) 91. 13x - 422 + 1x - 5212213x - 42132 92. 15 - 2x213217x - 822172 + 17x - 8231-22 Perform the indicated operations. 93. k2 + k 8k3 # 4 k2 - 1 94. 3r3 - 9r2 r2 - 9 , 8r3 r + 3 95. x2 + x - 2 x2 + 5x + 6 , x2 + 3x - 4 x2 + 4x + 3 96. 27m3 - n3 3m- n , 9m2 + 3mn + n2 9m2 - n2 97. p2 - 36q2 p2 - 12pq + 36q2 # p2 - 5pq - 6q2 p2 + 2pq + q2 98. 1 4y + 8 5y 99. m 4 - m + 3m m- 4 100. 3 x2 - 4x + 3 - 2 x2 - 1 101. p-1 + q-1 1 - 1pq2-1 102. 3 + 2m m2 - 4 5 m- 2 Simplify each expression. Assume all variables represent positive real numbers. 103. 2200 104. 23 16 105. 24 1250 106. -B16 3 107. -B3 2 5p2 108. B27y8 m3 109. 24 13 m 110. 24 8p2q5 # 24 2p3q 24 p5q2 111. A 23 2 + 4B A 23 22 - 423 2 + 16B 112. 325 - 2245 + 6280 113. 218m3 - 3m232m+ 52m3 114. 2 7 - 23 115. 6 3 - 22 116. k 2k - 3 Concept Check The following statements are incorrect. Correct each INCORRECT statement by changing the right side of the equation. 117. x1x2 + 52 = x3 + 5 118. -32 = 9 119. 1m223 = m5
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