# How do you factor x^3-27v^3?

##### 1 Answer
Apr 10, 2016

$\left(x - 3 v\right) \left({x}^{2} + 3 v x + 9 {v}^{2}\right)$

#### Explanation:

This problem is what is described as a Difference of Cubes

If we consider the equation:

${a}^{3} - {b}^{3}$ where $a$ and $b$ are perfect cubes, we can factorise the problem using the formula:

(a – b)(a^2 + ab + b^2)

In your case, if we consider the equation:

x^3−27v^3

We notice that not only are the $x$ and $y$ terms cubes, but 27 is also a cube $\left({3}^{3} = 27\right)$.

Therefore, if we substitute the values in to the Difference of Cubes formula, letting $x = a$ and $3 v = b$ we get:

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

Simplifying this we get the factored equation:

$\left(x - 3 v\right) \left({x}^{2} + 3 v x + 9 {v}^{2}\right)$