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-x^{2}-yx+12y^{2}
Consider -x^{2}-xy+12y^{2} as a polynomial over variable x.
\left(x+4y\right)\left(-x+3y\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -x^{2} and n divides the constant factor 12y^{2}. One such factor is x+4y. Factor the polynomial by dividing it by this factor.