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x^{2}+2yx-63y^{2}
Consider x^{2}+2xy-63y^{2} as a polynomial over variable x.
\left(x+9y\right)\left(x-7y\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 -63y^{2}. One such factor is x+9y. Factor the polynomial by dividing it by this factor.