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3a^{2}\left(2a-7b\right)+b^{2}\left(2a-7b\right)
Do the grouping 6a^{3}-21a^{2}b+2ab^{2}-7b^{3}=\left(6a^{3}-21a^{2}b\right)+\left(2ab^{2}-7b^{3}\right), and factor out 3a^{2} in the first and b^{2} in the second group.
\left(2a-7b\right)\left(3a^{2}+b^{2}\right)
Factor out common term 2a-7b by using distributive property.