Answer
$(y+2)^{2}(y-2)$
Work Step by Step
$ y^{3}+2y^{2}-4y-8\qquad$...factor in groups.
$=(y^{3}+2y^{2})+(-4y-8)$
$=y^{2}(y+2)-4(y+2)\qquad$...factor out the common binomial factor,$y+2$.
$=(y+2)(y^{2}-4)\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=(y+2)(y-2)(y+2)$
$=(y+2)^{2}(y-2)$
