Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - Chapter 6 Review Problem Set: 23

Answer

$(5x+y)(3x-2y)$

Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two variables whose product is $-30x^{2}y^{2}$ and whose sum is $-7xy$. A little searching determines that these numbers are $3xy$ and $-10xy$. Therefore, we can express the middle term, $-7xy$, as $(3xy-10xy)$ and proceed to factoring by grouping: $15x^{2}-7xy-2y^{2}$ =$15x^{2}+3xy-10xy-2y^{2}$ =$3x(5x+y)-2y(5x+y)$ =$(5x+y)(3x-2y)$
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