\[x^{2}(1 - x) + x(x - 1)^{2} = x^{2}(1 - x) + x \cdot\]
\[\cdot (1 - x)^{2} = (1 - x)\left( x^{2} + x(1 - x) \right) =\]
\[= (1 - x)\left( x^{2} + x - x^{2} \right) = x(1 - x)\]