Answer
$ y^4(y+2)^3(y+1)^2$
Work Step by Step
$Factor$ $the$ $expression$ $completely:$
$y^4(y+2)^3 + y^5(y+2)^4$
Factor out $y^4(y+2)^3$ from both terms
$y^4(y+2)^3[1 + y(y+2)]$
Distribute the y to $(y+2)$ in $[1 + y(y+2)]$
$= y^4(y+2)^3[1 + y^2 + 2y]$
$ = y^4(y+2)^3[y^2 + 2y + 1]$
Factor the trinomial in the bracket into binomials
$y^2 + 2y + 1$ = $(y+1)(y+1)$ = $(y+1)^2$
$ = y^4(y+2)^3(y+1)^2$
