Answer
$-2xy(9x-2yb)(2x-3y)$
Work Step by Step
$-36x^{3}y+62x^{2}y^{2}-12xy^{3}\qquad$...factor out the common term, $-2xy$.
$=-2xy(18x^{2}-31xy+6y^{2})$
... Searching for two factors of $ac=108$ whose sum is $b=-31,$
we find$\qquad-4$ and $-27.$
Rewrite the middle term and factor in pairs:
$=-2xy(18x^{2}-4xy-27xy+6y^{2})=$
$=-2xy[2x(9x-2y)-3y(9x-2y)]$
=$-2xy(9x-2yb)(2x-3y)$
