Section 1.7 Properties of Real Numbers and Simplifying Expressions 87 For Exercises 90–98, simplify by combining like terms. (See Examples 8–9.) 90. 91. 92. 5k 10k 4p 2p 7x2 14x2 2y2 5y2 3y2 2ab 5 3ab 2 8x3y 3 7 x3y 93. 94. 95. 2 5 3 5 6 5 96. 97. 98. 2.8z 8.1z 6 15.2 2t t For Exercises 99–126, simplify by clearing parentheses and combining like terms. (See Examples 10–12.) 99. 100. 101. 312x 42 10 214a 32 14 41w 32 12 512r 62 30 5 31x 42 4 213x 82 102. 103. 104. 312t 4w2 812t 4w2 515y 9z2 313y 6z2 21q 5u2 12q 8u2 105. 106. 107. 1 3 61x 3y2 16x 5y2 16t 92 10 108. 109. 110. 1015.1a 3.12 4 10013.14p 1.052 212 4m 21m 32 2m 111. 112. 113. 1 3 3b 41b 22 8b 12 3q2 114. 115. 116. 7n 21n 32 6 n 8k 41k 12 7 k 61x 32 12 41x 32 117. 118. 119. 51y 42 3 61y 72 0.216c 1.62 c 1.115 8x2 3.1 120. 121. 122. 6 238 312x 424 10x 3 533 41y 22 4 8y 123. 124. 1 3321z 12 51z 22 4 1 63312t 22 81t 22 4 125. 126. Expanding Your Skills For Exercises 127–134, determine if the expressions are equivalent. If two expressions are not equivalent, state why. 127. 3a b, b 3a 128. 4y 1, 1 4y 129. 2c 7, 9c 130. 5z 4, 9z 131. 132. 133. 134. 5x 3, 3 5x 6d 7, 7 6d 5x 3, 3 5x 8 2x, 2x 8 135. As a small child in school, the great mathematician Karl Friedrich Gauss (1777–1855) was said to have found the sum of the integers from 1 to 100 mentally: 1 2 3 4 p 99 100 Rather than adding the numbers sequentially, he added the numbers in pairs: 11 992 12 982 13 972 p 100 a. Use this technique to add the integers from 1 to 10. 1 2 3 4 5 6 7 8 9 10 b. Use this technique to add the integers from 1 to 20. 1 5 115 4p2 1 10 110p 52 1 2 110q 22 3 4 18 4q2 7 1 4 a b 3 4 a 5b
miller_beginning_intermediate_algebra_4e_ch1_3
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