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: 60

Answer

$(4m-p^2)(-4m^2-p)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $ -16m^3+4m^2p^2-4mp+p^3 ,$ 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} (-16m^3+4m^2p^2)-(4mp-p^3) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} -4m^2(4m-p^2)-p(4m-p^2) .\end{array} Factoring the $GCF= (4m-p^2) $ of the entire expression above results to \begin{array}{l}\require{cancel} (4m-p^2)(-4m^2-p) .\end{array}
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