Solve x^9-64a^3y^6=

$$x ^ { 9 } - 64 a ^ { 3 } y ^ { 6 } =$$

Factor

$$\left(x^{3}-4ay^{2}\right)\left(x^{6}+16a^{2}y^{4}+4ay^{2}x^{3}\right)$$

Solution Steps

Consider x^{9}-64a^{3}y^{6} as a polynomial over variable x. Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{9} and m divides the constant factor -64a^{3}y^{6}. One such factor is x^{3}-4ay^{2}. Factor the polynomial by dividing it by this factor.

$$\left(x^{3}-4ay^{2}\right)\left(x^{6}+16a^{2}y^{4}+4ay^{2}x^{3}\right)$$

Evaluate

$$x^{9}-64a^{3}y^{6}$$