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ISBN-10: 157685552X

ISBN-13: 9781576855522

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Extra info for 501 Algebra Questions, 2nd edition

Example text

Associate like terms. Perform the numerical operation in the parentheses. Zero is the identity element for addition. 77. Add 25 to each side of the equation. Use the commutative property for addition. Associate like terms. Perform the numerical operation in the parentheses. Zero is the identity element for addition. 78. Subtract 17 from both sides of the equation. Associate like terms. Change subtraction to addition and change the sign of the term that follows. Apply the rules for operating with signed numbers.

Adding a negative term is the same as subtracting a positive term. Use the commutative property of addition. Change addition to subtraction and change the sign of the term that follows. Either of the last two expressions is correct, but the second is the simpler. 33 Team-LRN 6(3m + −12) + −4(9m + 8) [6(3m + −12) = 6 · 3m + 6 · −12] [6 · 3m + 6 · −12 = 18m + −72] [−4(9m + 8) = −4 · 9m + −4 · 8] [−4 · 9m + −4 · 8 = −36m + −32] (18m + −72) + (−36m + −32) 18m + −72 + −36m + −32 18m + −36m + −72 + −32 (18m + −36m) + (−72 + −32) [18m + −36m = −18m] [−72 + −32 = −104] (−18m) + (−104) −18m + −104 −18m − +104 −104 + −18m −104 − (+18m) −104 − 18m 501 Algebra Questions 65.

Multiply from left to right. Evaluate the second term. Substitute the results into the numerical expression in the parentheses. Subtract. Substitute the result into the original expression. Multiply from left to right. The simpliﬁed value of the expression is as follows: 22 Team-LRN 10(−5)3 − 4(−5)2 [10(−5)3 = 10 · −5 · −5 · −5] [10 · −5 = (−50)] [(−50) · −5 = +250] [+250 · −5 = −1250] [4(−5)2 = 4 · −5 · −5] [4 · −5 = −20] [−20 · −5 = +100] −1250 − +100 −1250 + −100 [1250 + 100 = 1350] 10(−5)3 − 4(−5)2 = −1350 10b3 − 4b2 = −1,350 1 1 8(ᎏ2ᎏ)((3)3 − 2(ᎏ2ᎏ)) 1 1 ((3)3 − 2(ᎏ2ᎏ)) = (33 − 2 · ᎏ2ᎏ) [33 = 3 · 3 · 3 = 9 · 3 = 27] 1 [2 · ᎏ2ᎏ = 1] [(27) − (1)] [27 − 1 = 26] 1 8(ᎏ2ᎏ)(26) 1 [8 · ᎏ2ᎏ = 4] [4 · 26 = 104] 8y(a3 − 2y) = 104 501 Algebra Questions 49.