Answer
$ 3xy(3x+2y)(2x+5y)$
Work Step by Step
$ 18x^{3}y+57x^{2}y^{2}+30xy^{3}\qquad$...factor out the common term, $3xy$.
$=3xy(6x^{2}+19xy+10y^{2})$
... Searching for two factors of $ac=60$ whose sum is $b=19,$
we find$\qquad 4$ and $15.$
Rewrite the middle term and factor in pairs:
$=3xy(6x^{2}+4xy+15xy+10y^{2})=$
$=3xy[2x(3x+2y)+5y(3x+2y)]$
=$ 3xy(3x+2y)(2x+5y)$
