# Homework Help: Factorize the polynomial a^3 + b ^3 + c^3 - 3abc

1. Feb 6, 2008

### Trail_Builder

1. The problem statement, all variables and given/known data

factorise: $$a^3 + b^3 + c^3 - 3abc$$

2. Relevant equations

3. The attempt at a solution

I had a few random attempts and found that $$(a + b + c)$$ is factor, and then dividing the original equation by (a + b + c) yeilds $$a^2 + b^2 + c^2 - ab - ac - bc$$

I can't figure out how to factorise this quadratic. I tried solving for A and it either doesn;t work, or I did it wrong lol. short of trying a zillion different factors (i'd rather not, I'd prefer a more elegant solution), what can I do?

thanks.

2. Feb 6, 2008

### awvvu

I don't think you can. I stuck it into both maple and mathematica and they return the same factors as you have found.

3. Feb 6, 2008

### Trail_Builder

so I've factorised it as far as I can? :S

if so its a stupid problem lol. wouldve thought it would've given linear factors.