Answer
$(3x-2y)(5x+7y)$
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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$15x^{2}+11xy-14y^{2} =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=-210y^{2} $
2. $\quad$sum = $+11y\quad$... factors: $-10y$ and $+21y$
3. $\quad$ $15x^{2}+11xy-14y^{2} = (15x^{2}+21xy)+(-10xy-14y^{2} )$
4. $\quad$... $= 3x(5x+7y)+(-2y)(5x+7y) = (3x-2y)(5x+7y)$
Check by FOIL
$F:\quad 15x^{2}$
$O:\quad +21xy$
$I:\quad -10xy$
$L:\quad -14y^{2}$
$(3x-2y)(5x+7y)$ = $15x^{2}+11xy-14y^{2}$
