Answer
$ (3x+2y)(2x-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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$6x^{2}-5xy-6y^{2} =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=-36y^{2} $
2. $\quad$sum = $-5y\quad$... factors: $-9y$ and $+4y$
3. $\quad$ $6x^{2}-5xy-6y^{2} = (6x^{2}-9xy)+(4xy-6y^{2} )$
4. $\quad$... $= 3x(2x-3y)+(2y)(2x-3y) = (3x+2y)(2x-3y)$
Check by FOIL
$F:\quad 6x^{2}$
$O:\quad -9xy$
$I:\quad +4xy$
$L:\quad -6y^{2}$
$ (3x+2y)(2x-3y)$ = $6x^{2}-5xy-6y^{2}$
