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3m^{2}\left(3m-p^{2}\right)-p\left(3m-p^{2}\right)
Do the grouping 9m^{3}-3m^{2}p^{2}-3mp+p^{3}=\left(9m^{3}-3m^{2}p^{2}\right)+\left(-3mp+p^{3}\right), and factor out 3m^{2} in the first and -p in the second group.
\left(3m-p^{2}\right)\left(3m^{2}-p\right)
Factor out common term 3m-p^{2} by using distributive property.