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\frac{2y^{2}+y^{4}}{2}
Factor out \frac{1}{2}.
y^{2}\left(2+y^{2}\right)
Consider 2y^{2}+y^{4}. Factor out y^{2}.
\frac{y^{2}\left(2+y^{2}\right)}{2}
Rewrite the complete factored expression. Polynomial 2+y^{2} is not factored since it does not have any rational roots.