# How do you factor completely y^3 - 27?

Nov 22, 2015

${y}^{3} - 27 = \left(y - 3\right) \left({y}^{2} + 3 y + 9\right)$

#### Explanation:

One of the standard factor formulas is
$\textcolor{w h i t e}{\text{XXX}}$(x^3-a^3) = (x-a)(x^2+ax+a^2)#

In this case, substituting $y$ for $x$ and $27 = {3}^{3}$ for ${a}^{3}$
Note that in general we need to check the second factor $\left(y + 3 y + 9\right)$ for possible additional factors.
In this case the discriminant is $< 0$ which tells us no additional (Real) factors are available.