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m^{2}-4nm-12n^{2}
Consider m^{2}-4mn-12n^{2} as a polynomial over variable m.
\left(m-6n\right)\left(m+2n\right)
Find one factor of the form m^{k}+p, where m^{k} divides the monomial with the highest power m^{2} and p divides the constant factor -12n^{2}. One such factor is m-6n. Factor the polynomial by dividing it by this factor.