Разложите на множители xy^4-2y^4-xy+2y.

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

\[= y^{4}(x - 2) - y(x - 2) =\]

\[= (x - 2)\left( y^{4} - y \right) = y\left( y^{3} - 1 \right)(x - 2) =\]

\[= y(x - 2)(y - 1)(y^{2} + y + 1)\]