Answer
$ (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
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$12x^{2}+7xy-12y^{2} =...$
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) $ = $12x^{2}+7xy-12y^{2}$
