Solve x^3-64

$$x^3-64$$

Factor

$$\left(x-4\right)\left(x^{2}+4x+16\right)$$

Solution Steps

Rewrite x^{3}-64 as x^{3}-4^{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). Polynomial x^{2}+4x+16 is not factored since it does not have any rational roots.

$$\left(x-4\right)\left(x^{2}+4x+16\right)$$

Evaluate

$$x^{3}-64$$