# How do you factor x^3+8y^3?

Dec 17, 2015

${x}^{3} + 8 {y}^{3} = \left(x + 2 y\right) \left({x}^{2} - 2 x y + 4 {y}^{2}\right)$

#### Explanation:

In general:
$\textcolor{w h i t e}{\text{XXX}} \left({\textcolor{red}{a}}^{3} + {\textcolor{b l u e}{b}}^{3}\right) = \left(\textcolor{red}{a} + \textcolor{b l u e}{b}\right) \left({\textcolor{red}{a}}^{2} - \textcolor{red}{a} \textcolor{b l u e}{b} + {\textcolor{b l u e}{b}}^{2}\right)$

for various proofs of this see:
http://www.qc.edu.hk/math/Junior%20Secondary/sum%20of%20two%20cubes.htm

$\left({x}^{3} + 8 {y}^{3}\right) = \left({\textcolor{red}{x}}^{3} + {\textcolor{b l u e}{\left(2 y\right)}}^{3}\right)$

Substituting
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{x}$ for $\textcolor{red}{a}$
and
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{2 y}$ for $\textcolor{b l u e}{b}$
in the general form
$\textcolor{w h i t e}{\text{XXX}}$gives the answer above.