Answer
$2xy^{3}(9x-y)$
Work Step by Step
The Greatest Common Factor of $18y^3x^2$ and $2xy^4$ is $2xy^3$. We factor it out:
$$18y^{3}x^{2}-2xy^{4}=2xy^{3}(9x-y).$$ The original expression is now fully factorized.
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