Answer
$13x^3y(y+4)(y-1)$.
Work Step by Step
The given expression is
$=13x^3y^3+39x^3y^2-52x^3y$
Factor out $13x^3y$.
$=13x^3y(y^2+3y-4)$
Rewrite $3y$ as $4y-1y$.
$=13x^3y(y^2+4y-1y-4)$
Group terms.
$=13x^3y[(y^2+4y)+(-1y-4)]$
Factor from each group.
$=13x^3y[y(y+4)-1(y+4)]$
Factor out $(y+4)$.
$=13x^3y(y+4)(y-1)$.
