# How do you simplify x^3+3 ?

Apr 30, 2016

${x}^{3} + 3 = \left(x + \sqrt[3]{3}\right) \left({x}^{2} - \sqrt[3]{3} x + \sqrt[3]{9}\right)$

#### Explanation:

This is already in simplest form unless you count factorisation.

We can treat this expression as a sum of cubes and use the sum of cubes identity:

${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$

with $a = x$ and $b = \sqrt[3]{3}$ as follows:

${x}^{3} + 3$

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

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

$= \left(x + \sqrt[3]{3}\right) \left({x}^{2} - \sqrt[3]{3} x + \sqrt[3]{9}\right)$