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a^{2}\left(a+b^{3}\right)-b\left(a+b^{3}\right)
Do the grouping a^{3}+a^{2}b^{3}-ab-b^{4}=\left(a^{3}+a^{2}b^{3}\right)+\left(-ab-b^{4}\right), and factor out a^{2} in the first and -b in the second group.
\left(a+b^{3}\right)\left(a^{2}-b\right)
Factor out common term a+b^{3} by using distributive property.