Answer
$2y^{2}(y-1)(y^{2}+y+1)$
Work Step by Step
$ 2y^{5}-2y^{2}\qquad$...factor out the common term, $2y^{2}$
$=2y^{2}(y^{3}-1)\qquad$...use the difference of two cubes: $\mathrm{A}^{3}-\mathrm{B}^{3} = (\mathrm{A}-\mathrm{B})(\mathrm{A}^{2} + \mathrm{A}\mathrm{B} + B^{2})$
$=2y^{2}(y^{3}-1^{3})$
$=2y^{2}(y-1)(y^{2}+y+1)$
