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\frac{4xy^{3}-18x^{2}y^{2}+54xy^{2}-27x^{3}y^{2}-18xy^{2}z}{6}
Factor out \frac{1}{6}.
xy^{2}\left(4y-18x+54-27x^{2}-18z\right)
Consider 4xy^{3}-18x^{2}y^{2}+54xy^{2}-27x^{3}y^{2}-18xy^{2}z. Factor out xy^{2}.
\frac{xy^{2}\left(4y-18x+54-27x^{2}-18z\right)}{6}
Rewrite the complete factored expression.