By Alex Bellos

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107. 109. 111. 113. 114. 115. 116. 117. 118. 119. (b) a is shown in the following figure. x x x x x 1 1 1 1 1 x (a) x x 1 b b (c) a a a a b b b b b (d) b b 1 1 1 1 b 121. 122. 123. 124. a 2 Ϫ b 2 ϭ ͑a ϩ b͒͑a Ϫ b͒ a 2 ϩ 2ab ϩ b 2 ϭ ͑a ϩ b͒ 2 a 2 ϩ 2a ϩ 1 ϭ ͑a ϩ 1͒ 2 ab ϩ a ϩ b ϩ 1 ϭ ͑a ϩ 1͒͑b ϩ 1͒ x 125. 126. 127. 128. 3x 2 ϩ 7x ϩ 2 ϭ ͑3x ϩ 1͒͑x ϩ 2͒ x 2 ϩ 4x ϩ 3 ϭ ͑x ϩ 3͒͑x ϩ 1͒ 2x 2 ϩ 7x ϩ 3 ϭ ͑2x ϩ 1͒͑x ϩ 3͒ x 2 ϩ 3x ϩ 2 ϭ ͑x ϩ 2͒͑x ϩ 1͒ 1 GEOMETRY In Exercises 129–132, write an expression in factored form for the area of the shaded portion of the figure.

5 x3 ϩ x2 Ϫ x Ϫ 5 4 x ϩ 3x ϩ 4 x ϩ 9 ͑t Ϫ 1͒ 2 Ϫ 49 108. ͑x 2 ϩ 1͒ 2 Ϫ 4x 2 ͑x 2 ϩ 8͒ 2 Ϫ 36x 2 110. 2t 3 Ϫ 16 5x 3 ϩ 40 112. 4x͑2x Ϫ 1͒ ϩ ͑2x Ϫ 1͒ 2 5͑3 Ϫ 4x͒ 2 Ϫ 8͑3 Ϫ 4x͒͑5x Ϫ 1͒ 2͑x ϩ 1͒͑x Ϫ 3͒ 2 Ϫ 3͑x ϩ 1͒ 2͑x Ϫ 3͒ 7͑3x ϩ 2͒ 2͑1 Ϫ x͒ 2 ϩ ͑3x ϩ 2͒͑1 Ϫ x͒3 7x͑2͒͑x 2 ϩ 1͒͑2x͒ Ϫ ͑x2 ϩ 1͒ 2͑7͒ 3͑x Ϫ 2͒2͑x ϩ 1͒4 ϩ ͑x Ϫ 2͒ 3͑4͒͑x ϩ 1͒ 3 2x͑x Ϫ 5͒ 4 Ϫ x 2͑4͒͑x Ϫ 5͒ 3 5͑x6 ϩ 1͒4͑6x5͒͑3x ϩ 2͒3 ϩ 3͑3x ϩ 2͒2͑3͒͑x6 ϩ 1͒5 x2 120. ͑x2 ϩ 1͒4 Ϫ ͑x 2 ϩ 1͒5 2 89. 91. 93. 95. 97. 99. 101. 103. 105. 107. 109. 111.

58. 59. 60. 61. 62. Add Ϫ ϩ 8 and Ϫ 4. 5 3 Add 2x Ϫ 3x ϩ 2x ϩ 3 and 4x 3 ϩ x Ϫ 6. Subtract x Ϫ 3 from 5x 2 Ϫ 3x ϩ 8. 6t 4 Ϫ 2t 2. Multiply ͑x ϩ 7͒ and ͑2x ϩ 3͒. Multiply ͑3x ϩ 1͒ and ͑x Ϫ 5͒. Multiply ͑x2 ϩ 2x ϩ 3͒ and ͑x2 Ϫ 2x ϩ 3͒. Multiply ͑x2 ϩ x Ϫ 4͒ and ͑x2 Ϫ 2x ϩ 1͒. 7x 3 2x 2 Ϫ3x3 In Exercises 63–100, multiply or find the special product. 63. 65. 67. 69. 71. 73. 75. 77. 79. 80. 81. 82. 83. 84. 85. 87. 89. 91. 93. 94. 95. 96. 97. 98. 99. 100. ͑x ϩ 3͒͑x ϩ 4͒ 64. ͑x Ϫ 5͒͑x ϩ 10͒ ͑3x Ϫ 5͒͑2x ϩ 1͒ 66.