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