Solve 2x^6-16y^9=

$$2 x ^ { 6 } - 16 y ^ { 9 } =$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(x^{6}-8y^{9}\right)$$

Consider x^{6}-8y^{9}. Rewrite x^{6}-8y^{9} as \left(x^{2}\right)^{3}-\left(2y^{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).

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

Rewrite the complete factored expression.

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

Evaluate

$$2\left(x^{6}-8y^{9}\right)$$