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2\left(m^{4}+3\right)-a\left(m^{4}+3\right)
Do the grouping 2m^{4}+6-am^{4}-3a=\left(2m^{4}+6\right)+\left(-am^{4}-3a\right), and factor out 2 in the first and -a in the second group.
\left(m^{4}+3\right)\left(2-a\right)
Factor out common term m^{4}+3 by using distributive property. Polynomial m^{4}+3 is not factored since it does not have any rational roots.