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6\left(4y^{8}+y^{6}\right)
Factor out 6.
y^{6}\left(4y^{2}+1\right)
Consider 4y^{8}+y^{6}. Factor out y^{6}.
6y^{6}\left(4y^{2}+1\right)
Rewrite the complete factored expression. Polynomial 4y^{2}+1 is not factored since it does not have any rational roots.