Разложите на множители x^3+8y^3-2x^2y-4xy^2.

\[x^{3} + 8y^{3} - 2x^{2}y - 4xy^{2} =\]

\[= (x + 2y)\left( x^{2} - 2xy + 4y^{2} \right) - 2xy(x + 2y) =\]

\[= (x + 2y)\left( x^{2} - 2xy + 4y^{2} - 2xy \right) =\]

\[= (x + 2y)\left( x^{2} - 4xy + 4y^{2} \right) =\]

\[= (x + 2y)(x - 2y)^{2}\]