Answer
$(3x-7y)(x+y)$
Work Step by Step
Treat y as a constant, and the trinomial as $ax^{2}+bx+c$.
$(3)x^{2}-(4y)x-7y^{2}$
For trinomials $ax^{2}+bx+c$, we search for factors of $ac$ whose sum is $b.$ If we find a pair, rewrite $bx$ and factor in pairs:
Here we search for factors of $ac=-21y^2$, whose sum is $-4y.$
We find $-7y$ and $ +3y, $
$3x^{2}-4xy-7y^{2}=3x^{2}-7xy+3xy-7y^{2}$
$=x(3x-7y)+y(3x-7y)$
= $(3x-7y)(x+y)$
