## Precalculus: Mathematics for Calculus, 7th Edition

$y^4(y+2)^3(y+1)^2$
$Factor$ $the$ $expression$ $completely:$ $y^4(y+2)^3 + y^5(y+2)^4$ 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 $y^2 + 2y + 1$ = $(y+1)(y+1)$ = $(y+1)^2$ $= y^4(y+2)^3(y+1)^2$