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3\left(a+2b\right)+4ab\left(a+2b\right)
Do the grouping 3a+6b+4a^{2}b+8ab^{2}=\left(3a+6b\right)+\left(4a^{2}b+8ab^{2}\right), and factor out 3 in the first and 4ab in the second group.
\left(a+2b\right)\left(3+4ab\right)
Factor out common term a+2b by using distributive property.