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