Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Section 5.1 - Greatest Common Factors and Factoring by Grouping - 5.1 Exercises: 65

Answer

$(1-a)(1-b) $

Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $ 1-a+ab-b ,$ such that the factored form of the groupings will result to a factor common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression. $\bf{\text{Solution Details:}}$ Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (1-a)+(ab-b) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} (1-a)+b(a-1) \\\\= (1-a)-b(1-a) .\end{array} Factoring the $GCF= (1-a) $ of the entire expression above results to \begin{array}{l}\require{cancel} (1-a)(1-b) .\end{array}
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