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4\left(3y^{10}+y^{6}\right)
Factor out 4.
y^{6}\left(3y^{4}+1\right)
Consider 3y^{10}+y^{6}. Factor out y^{6}.
4y^{6}\left(3y^{4}+1\right)
Rewrite the complete factored expression. Polynomial 3y^{4}+1 is not factored since it does not have any rational roots.