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2\left(4y^{6}+y^{3}\right)
Factor out 2.
y^{3}\left(4y^{3}+1\right)
Consider 4y^{6}+y^{3}. Factor out y^{3}.
2y^{3}\left(4y^{3}+1\right)
Rewrite the complete factored expression. Polynomial 4y^{3}+1 is not factored since it does not have any rational roots.