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3x^{2}+8yx-3y^{2}
Consider 3x^{2}+8xy-3y^{2} as a polynomial over variable x.
\left(3x-y\right)\left(x+3y\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 3x^{2} and n divides the constant factor -3y^{2}. One such factor is 3x-y. Factor the polynomial by dividing it by this factor.