# How do you factor x^3 - 1000?

Feb 10, 2016

Factors are $\left(a - 10\right) \cdot \left({a}^{2} - 10 a + 100\right)$

#### Explanation:

The polynomial is of the type ${a}^{3} - {b}^{3}$ whose standard factors are $\left(a - b\right) \cdot \left({a}^{2} - a \cdot b + {b}^{2}\right)$, as $1000$ is nothing but.${10}^{3}$.

Thus the polynomial can be expressed as ${x}^{3} - {10}^{3}$ and its factors will be

$\left(a - 10\right) \cdot \left({a}^{2} - a \cdot 10 + {10}^{2}\right)$ or

$\left(a - 10\right) \cdot \left({a}^{2} - 10 a + 100\right)$.