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-y^{3}x^{6}+1000
Consider 1000-x^{6}y^{3} as a polynomial over variable x.
\left(yx^{2}-10\right)\left(-y^{2}x^{4}-10yx^{2}-100\right)
Find one factor of the form ky^{m}x^{n}+p, where ky^{m}x^{n} divides the monomial with the highest power -y^{3}x^{6} and p divides the constant factor 1000. One such factor is yx^{2}-10. Factor the polynomial by dividing it by this factor.