Answer
$2x(x+1)(x^2-2)$
Work Step by Step
The given expression, $
2x^4+2x^3-4x^2-4x
,$ simplifies to
\begin{array}{l}\require{cancel}
2x(x^3+x^2-2x-2)
\\\\=
2x[(x^3+x^2)-(2x+2)]
\\\\=
2x[x^2(x+1)-2(x+1)]
\\\\=
2x[(x+1)(x^2-2)]
\\\\=
2x(x+1)(x^2-2)
.\end{array}