Solve 8x^3-64y^3

$$8 x ^ { 3 } - 64 y ^ { 3 }$$

Factor

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

Solution Steps

Factor out 8.

$$8\left(x^{3}-8y^{3}\right)$$

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

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

Rewrite the complete factored expression.

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

Evaluate

$$8\left(x^{3}-8y^{3}\right)$$