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