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