Разложите на множители: x^3+y^3+2xy(x+y).

\[x^{3} + y^{3} + 2xy(x + y) =\]

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

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

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