# How do you factor #64r^3 - 27#?

##### 2 Answers

Use the difference of cubes formula (and the quadratic formula if you allow for complex numbers) to find that

#### Explanation:

The difference of cubes formula states that

(Try multiplying the right hand side to verify this).

In this case, that gives us

If we are only consider real numbers, then we are done. If we are allowing for complex numbers, then we can continue factoring using the quadratic formula on the remaining quadratic expression.

Thus, making sure to multiply by

Hence factors are given by

#### Explanation:

As the function

Using this,

=

It is obvious that this cannot be factorized further, as the determinant

Hence factors are given by