Intermediate Algebra (12th Edition)

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

Chapter 5 - Section 5.3 - Special Factoring - 5.3 Exercises: 63

Answer

$(5y^2+z)(25y^4-5y^2z+z^2)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ 125y^6+z^3 ,$ use the factoring of the sum/difference of $2$ cubes. $\bf{\text{Solution Details:}}$ Using the factoring of the sum/difference of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ or by $a^3-b^3=(a-b)(a^2+ab+b^2),$ the expression above is equivalent to \begin{array}{l}\require{cancel} (5y^2+z)[(5y^2)^2-5y^2(z)+(z)^2] \\\\= (5y^2+z)(25y^4-5y^2z+z^2) .\end{array}
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