I need help to simplify the following.

Question

I need to know how to simplify the following equation u^3-8w^3?

Answer 1

Well...one may see that each term can be represented as the "cube" of a simpler term, i.e. we may write:

 

u³ - 8w³ = (u)³ - (2w)³

 

Then, using the formula known as the "difference of cubes", which states:

 

a³ - b³ = (a-b) * (a² + ab + b²)

 

We see that:

 

u³-8w³ = (u)³ - (2w)³ = (u-2w) * ( u² + u*2w + (2w)²) 

 = (u-2w) * (u² +2uw + 4w²)