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m^{2}+\left(2n-3\right)m+n^{2}-3n
Consider m^{2}+2mn+n^{2}-3m-3n as a polynomial over variable m.
\left(m+n\right)\left(m+n-3\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 n^{2}-3n. One such factor is m+n. Factor the polynomial by dividing it by this factor.