Solve 8x^6+8y^6=

$$8 x ^ { 6 } + 8 y ^ { 6 } =$$

Factor

$$8\left(x^{2}+y^{2}\right)\left(x^{4}-x^{2}y^{2}+y^{4}\right)$$

Solution Steps

Factor out 8.

$$8\left(x^{6}+y^{6}\right)$$

Consider x^{6}+y^{6}. Rewrite x^{6}+y^{6} as \left(x^{2}\right)^{3}+\left(y^{2}\right)^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(x^{2}+y^{2}\right)\left(x^{4}-x^{2}y^{2}+y^{4}\right)$$

Rewrite the complete factored expression.

$$8\left(x^{2}+y^{2}\right)\left(x^{4}-x^{2}y^{2}+y^{4}\right)$$

Evaluate

$$8\left(x^{6}+y^{6}\right)$$