Answer
$(y+2)(y^{2}+y+1)$
Work Step by Step
$(y+1)^{3}+1\qquad$...recognize a sum of two cubes:$\mathrm{A}^{3}+\mathrm{B}^{3} = (\mathrm{A}+\mathrm{B})(\mathrm{A}^{2} - \mathrm{A}\mathrm{B} + B^{2})$
$=(y+1)^{3}+1^{3}$
$=(y+1+1)((y+1)^{2}-(y+1)\cdot 1+1^{2})\qquad$...simplify.
$=(y+2)(y^{2}+2y+1-y-1+1)$
$=(y+2)(y^{2}+y+1)$
