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