By Soo T. Tan

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X2 Ϫ 2x Ϫ 15 111. 3x2 Ϫ 6x Ϫ 24 112. 3x2 Ϫ 4x Ϫ 4 113. 12x2 Ϫ 2x Ϫ 30 114. (x ϩ y)2 Ϫ 1 115. 9x2 Ϫ 16y2 116. 8a2 Ϫ 2ab Ϫ 6b2 117. x6 ϩ 125 118. x3 Ϫ 27 78. 3(2a Ϫ b) Ϫ 4(b Ϫ 2a) 79. x Ϫ {2x Ϫ [Ϫx Ϫ (1 Ϫ x)]} 80. 3x2 Ϫ {x2 ϩ 1 Ϫ x[x Ϫ (2x Ϫ 1)]} ϩ 2 1 1 81. ¢ Ϫ 1 ϩ e≤ Ϫ ¢Ϫ Ϫ 1 ϩ eϪ1≤ 3 3 3 1 1 1 82. Ϫ y Ϫ x ϩ 100 ϩ x ϩ y Ϫ 120 4 4 2 4 1 3 83. 318 ϩ 8 Ϫ 21y ϩ 1x Ϫ 1y 2 4 In Exercises 119–126, perform the indicated operations and simplify each expression. 119. (x2 ϩ y2)x Ϫ xy(2y) 120. 2kr(R Ϫ r) Ϫ kr 2 8 2 16 16 84.

1 ϩ e≤ Ϫ ¢Ϫ Ϫ 1 ϩ eϪ1≤ 3 3 3 1 1 1 82. Ϫ y Ϫ x ϩ 100 ϩ x ϩ y Ϫ 120 4 4 2 4 1 3 83. 318 ϩ 8 Ϫ 21y ϩ 1x Ϫ 1y 2 4 In Exercises 119–126, perform the indicated operations and simplify each expression. 119. (x2 ϩ y2)x Ϫ xy(2y) 120. 2kr(R Ϫ r) Ϫ kr 2 8 2 16 16 84. x2 ϩ x ϩ x2 Ϫ x Ϫ 2x ϩ 2 9 3 3 3 121. 2(x Ϫ 1)(2x ϩ 2)3[4(x Ϫ 1) ϩ (2x ϩ 2)] 85. (x ϩ 8)(x Ϫ 2) 86. (5x ϩ 2)(3x Ϫ 4) 122. 5x2(3x2 ϩ 1)4(6x) ϩ (3x2 ϩ 1)5(2x) 87. (a ϩ 5)2 88. (3a Ϫ 4b)2 89. (x ϩ 2y)2 90. (6 Ϫ 3x)2 91. (2x ϩ y)(2x Ϫ y) 92.

A cable is to be laid connecting the relay station with the experimental station. 00 per running foot, find the total cost for laying the cable. y (feet) M(0, 3000) x (feet) O Q(2000, 0) S(10,000, 0) FIGURE 14 Cable connecting relay station S to experimental station M Solution The length of cable required on land is given by the distance from S to Q. This distance is (10,000 Ϫ 2000), or 8000 feet. Next, we see that the length of cable required underwater is given by the distance from M to Q. 55 feet.