Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set - Page 344: 65



Work Step by Step

The given expression, $ -12-x^2y^2-8xy ,$ can be re-written as \begin{array}{l} -x^2y^2-8xy-12 \\\\= -(x^2y^2+8xy+12) .\end{array} The two numbers whose product is $ac= 1(12)=12 $ and whose sum is $b= 8 $ are $\{ 2,6 \}$. Using these two numbers to decompose the middle term of the expression, $ -(x^2y^2+8xy+12) ,$ then the factored form is \begin{array}{l} -(x^2y^2+2xy+6xy+12) \\\\= -[(x^2y^2+2xy)+(6xy+12)] \\\\= -[xy(xy+2)+6(xy+2)] \\\\= -[(xy+2)(xy+6)] \\\\= -(xy+2)(xy+6) .\end{array}
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