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81x^{2}+9x-y^{2}+y
Consider 81x^{2}-y^{2}+9x+y as a polynomial over variable x.
\left(9x+y\right)\left(9x-y+1\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 81x^{2} and n divides the constant factor -y^{2}+y. One such factor is 9x+y. Factor the polynomial by dividing it by this factor.