Answer
$(3x-5y)(2x+y)$
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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$6x^{2}-7xy-5y^{2} =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=-30y^{2} $
2. $\quad$sum = $-7y\quad$... factors: $-10y$ and $+3y$
3. $\quad$ $6x^{2}-7xy-5y^{2} = (6x^{2}+3xy)+(-10xy-5y^{2} )$
4. $\quad$... $= 3x(2x+y)+(-5y)(2x+y) = (3x-5y)(2x+y)$
Check by FOIL
$F:\quad 6x^{2}$
$O:\quad +3xy$
$I:\quad -10xy$
$L:\quad -5y^{2}$
$(3x-5y)(2x+y)$ = $6x^{2}-7xy-5y^{2}$
