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m^{2}+5nm+4n^{2}
Consider m^{2}+5mn+4n^{2} as a polynomial over variable m.
\left(m+4n\right)\left(m+n\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 4n^{2}. One such factor is m+4n. Factor the polynomial by dividing it by this factor.