# Thread: Factoring a sum or difference of cube

1. ## Factoring a sum or difference of cube

How do you factor this cube:

$(x+5)^3 - (2x+1)^3$

2. Originally Posted by Devi09
How do you factor this cube:

$(x+5)^3 - (2x+1)^3$
$(a^3-b^3)=(a-b)(a^2+ab+b^2)$

Let $a=x+5$ and $b=2x+1$.

It isn't pretty!

3. As these are cubics you may want to consider expanding using the binomial theorem and collecting like terms.

Unless, of course, you've been instructed to use the difference of two cubes