Intermediate Algebra (12th Edition)

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

Chapter 5 - Chapter 5 Test: 2


$5x^2y^3 \left( 2y^3-1-5x^3 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Get the $GCF$ of the given expression, $ 10x^2y^5-5x^2y^3-25x^5y^3 .$ Divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient. $\bf{\text{Solution Details:}}$ The $GCF$ of the constants of the terms $\{ 10,5,25 \}$ is $ 5 $ since it is the highest number that can divide all the given constants. The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{ x^2y^5,x^2y^3,x^5y^3 \}$ is $ x^2y^3 .$ Hence, the entire expression has $GCF= 5x^2y^3 .$ Factoring the $GCF= 5x^2y^3 ,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 5x^2y^3 \left( \dfrac{10x^2y^5}{5x^2y^3}-\dfrac{5x^2y^3}{5x^2y^3}-\dfrac{25x^5y^3}{5x^2y^3} \right) \\\\= 5x^2y^3 \left( 2y^3-1-5x^3 \right) .\end{array}
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