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8\left(4x^{9}y^{3}-xy^{5}\right)
Factor out 8.
xy^{3}\left(4x^{8}-y^{2}\right)
Consider 4x^{9}y^{3}-xy^{5}. Factor out xy^{3}.
\left(2x^{4}-y\right)\left(2x^{4}+y\right)
Consider 4x^{8}-y^{2}. Rewrite 4x^{8}-y^{2} as \left(2x^{4}\right)^{2}-y^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
8xy^{3}\left(2x^{4}-y\right)\left(2x^{4}+y\right)
Rewrite the complete factored expression.