Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.3 - Factoring Trinomials Whose Leading Coefficient is Not 1 - Exercise Set - Page 444: 58


$ (3x+4y)(4x-3y) $

Work Step by Step

Factoring by grouping: 1. Multiply the leading coefficient, a, and the constant, c. 2. Find the factors of ac whose sum is b. 3. Rewrite the middle term, bx, as a sum or difference using the factors from step 2. 4. Factor by grouping --- $12x^{2}+7xy-12y^{2} =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad$"$ac$"$=-144y^{2} \qquad$ $...(144=12\times 12-3\times 4\times 3\times 4=9\times 16) $ 2. $\quad$sum = $+7xy\quad$... factors: $+16y$ and $-9y$ 3. $\quad$ $12x^{2}+7xy-12y^{2} = (12x^{2}-9xy)+( 16xy+12y^{2})$ 4. $\quad$... $= 3x(4x-3y)+(4y)(4x-3y) = (3x+4y)(4x-3y) $ Check by FOIL $F:\quad 12x^{2}$ $O:\quad -9xy$ $I:\quad +16xy$ $L:\quad +12y^{2}$ $ (3x+4y)(4x-3y) $ = $12x^{2}+7xy-12y^{2}$
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