Answer
$(2x-y)(x+2y)$
Work Step by Step
In accordance with the rules of factoring trinomials, we need to find two variables whose product is $-4x^{2}y^{2}$ and whose sum is $3xy$. A little searching determines that these numbers are $-1xy$ and $4xy$. Therefore, we can express the middle term $3xy$ as $(-1xy+4xy)$ and proceed to factoring by grouping:
$2x^{2}+3xy-2y^{2}$
=$2x^{2}-1xy+4xy-2y^{2}$
=$x(2x-y)+2y(2x-y)$
=$(2x-y)(x+2y)$
