Answer
$(x+y)(3x+2y)$
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: $3y$ and $2y$
3. $\quad$ $3x^{2}+5xy+2y^{2} = (3x^{2}+3xy)+(2xy+2y^{2} )$
4. $\quad$... $= 3x(x+y)+(2y)(x+y) =(x+y)(3x+2y)$
Check by FOIL
$F:\quad 3x^{2}$
$O:\quad +2xy$
$I:\quad +3xy$
$L:\quad +2y^{2}$
$(x+y)(3x+2y)$ = $3x^{2}+5xy+2y^{2}$
