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a^{2}\left(a+1\right)-3b\left(a+1\right)
Do the grouping a^{3}+a^{2}-3ab-3b=\left(a^{3}+a^{2}\right)+\left(-3ab-3b\right), and factor out a^{2} in the first and -3b in the second group.
\left(a+1\right)\left(a^{2}-3b\right)
Factor out common term a+1 by using distributive property.