Answer
$18y^{3}x^{2}-2xy^{4}=2yx^{3}(9x-y)$.
Work Step by Step
Can begin by factoring out a factor of 2 hence $18y^{3}x^{2}-2xy^{4}=2(9y^{3}x^{2}-xy^{4})$.
Can also factor out a factor of $y^3$ hence $2(9y^{3}x^{2}-xy^{4})=2y^{3}(9x^{2}-xy)$.
Can then also factor out an $x$ hence $2y^{3}(9x^{2}-xy)=2yx^{3}(9x-y)$.
The original expression is now fully factorized.
