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10\left(y^{3}+y^{7}\right)
Factor out 10.
y^{3}\left(1+y^{4}\right)
Consider y^{3}+y^{7}. Factor out y^{3}.
10y^{3}\left(1+y^{4}\right)
Rewrite the complete factored expression. Polynomial 1+y^{4} is not factored since it does not have any rational roots.