\[y^{5} - 2y^{3} + y =\]
\[= y\left( y^{4} - 2y^{2} + 1 \right) =\]
\[= y\left( y^{2} - 1 \right)^{2} =\]
\[= y(y - 1)^{2}(y + 1)^{2}.\]