# How do you factor: y= x^3+1/8 ?

Oct 3, 2016

Sum of cubes.
$\left(x + \frac{1}{2}\right) \left({x}^{2} - \frac{x}{2} + \frac{1}{4}\right)$

#### Explanation:

It helps to know the common squares and cubes!
This expression is the sum of two cubes.
It factors as

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

Following the same pattern:

${x}^{3} + \frac{1}{8} = \left(x + \frac{1}{2}\right) \left({x}^{2} - \frac{x}{2} + \frac{1}{4}\right)$