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