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

##### 1 Answer

Apr 23, 2016

#### Explanation:

The difference of cubes identity can be written:

#a^3-b^3=(a-b)(a^2+ab+b^2)#

We can use this with

#64r^3-p^3#

#=(4r)^3-p^3#

#=(4r-p)((4r)^2+(4r)p+p^2)#

#=(4r-p)(16r^2+4rp+p^2)#

This cannot be factored further with Real coefficients.

If you allow Complex coeffients then it can be factored a little further:

#= (4r-p)(4r-omega p)(4r-omega^2 p)#

where