# How do you factor  (x^3)- 100 = 0?

Jan 19, 2018

$\left(x - \sqrt[3]{100}\right) \left({x}^{2} + x \sqrt[3]{100} + {\left(\sqrt[3]{100}\right)}^{2}\right) = 0$

#### Explanation:

We could use the fact that ${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$

So we could rewrite ${x}^{3} - 100 = 0$ as
${x}^{3} - {\left(\sqrt[3]{100}\right)}^{3} = 0 \implies \left(x - \sqrt[3]{100}\right) \left({x}^{2} + x \sqrt[3]{100} + {\left(\sqrt[3]{100}\right)}^{2}\right) = 0$

To find the values of $x$, you could solve the following equations:
$x - \sqrt[3]{100} = 0$ and ${x}^{2} + x \sqrt[3]{100} + {\left(\sqrt[3]{100}\right)}^{2} = 0$.