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3\left(x^{2}y-6xy^{2}+9y^{3}\right)
Factor out 3.
y\left(x^{2}-6xy+9y^{2}\right)
Consider x^{2}y-6xy^{2}+9y^{3}. Factor out y.
\left(x-3y\right)^{2}
Consider x^{2}-6xy+9y^{2}. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=x and b=3y.
3y\left(x-3y\right)^{2}
Rewrite the complete factored expression.