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x^{2}-8x-9-y^{2}-10y
Consider x^{2}-8x-9-y^{2}-10y as a polynomial over variable x.
\left(x+y+1\right)\left(x-y-9\right)
Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{2} and m divides the constant factor -y^{2}-10y-9. One such factor is x+y+1. Factor the polynomial by dividing it by this factor.