Factorize the polynomial a^3 + b ^3 + c^3 - 3abc

[Trail_Builder]

Homework Statement

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

Homework Equations

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.

 

[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.

 

[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.