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a\left(2ab-1\right)+2b\left(2ab-1\right)
Do the grouping 2a^{2}b-a-2b+4ab^{2}=\left(2a^{2}b-a\right)+\left(-2b+4ab^{2}\right), and factor out a in the first and 2b in the second group.
\left(2ab-1\right)\left(a+2b\right)
Factor out common term 2ab-1 by using distributive property.