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: 54

Answer

$(r+3w)(r-3t)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $ r^2-9tw+3rw-3rt ,$ 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 third terms and the second and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (r^2+3rw)-(9tw+3rt) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} r(r+3w)-3t(3w+r) \\\\= r(r+3w)-3t(r+3w) .\end{array} Factoring the $GCF= (r+3w) $ of the entire expression above results to \begin{array}{l}\require{cancel} (r+3w)(r-3t) .\end{array}
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