Solve x^9-y^9=

$$x ^ { 9 } - y ^ { 9 } =$$

Factor

$$\left(x-y\right)\left(x^{2}+xy+y^{2}\right)\left(x^{6}+x^{3}y^{3}+y^{6}\right)$$

Solution Steps

Rewrite x^{9}-y^{9} as \left(x^{3}\right)^{3}-\left(y^{3}\right)^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(x^{3}-y^{3}\right)\left(x^{6}+x^{3}y^{3}+y^{6}\right)$$

Consider x^{3}-y^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(x-y\right)\left(x^{2}+xy+y^{2}\right)$$

Rewrite the complete factored expression.

$$\left(x-y\right)\left(x^{2}+xy+y^{2}\right)\left(x^{6}+x^{3}y^{3}+y^{6}\right)$$

Evaluate

$$x^{9}-y^{9}$$