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4am\left(m^{2}-3n\right)-\left(m^{2}-3n\right)
Do the grouping 4am^{3}-12amn-m^{2}+3n=\left(4am^{3}-12amn\right)+\left(-m^{2}+3n\right), and factor out 4am in the first and -1 in the second group.
\left(m^{2}-3n\right)\left(4am-1\right)
Factor out common term m^{2}-3n by using distributive property.