Intermediate Algebra (12th Edition)

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

Chapter 5 - Chapter 5 Test: 3

Answer

$(b+3)(x+y)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $ 3x+by+bx+3y ,$ such that the factored form of the groupings will result to a factor that is 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 third terms and the second and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (3x+bx)+(by+3y) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} x(3+b)+y(b+3) \\\\= x(b+3)+y(b+3) .\end{array} Factoring the $GCF= (b+3) $ of the entire expression above results to \begin{array}{l}\require{cancel} (b+3)(x+y) .\end{array}
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