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-a^{2}+\left(4+2m\right)a-4m-m^{2}
Consider 4a-a^{2}-4m+2am-m^{2} as a polynomial over variable a.
\left(m-a\right)\left(-m+a-4\right)
Find one factor of the form ka^{n}+p, where ka^{n} divides the monomial with the highest power -a^{2} and p divides the constant factor -m^{2}-4m. One such factor is m-a. Factor the polynomial by dividing it by this factor.