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

  1. Feb 6, 2008 #1
    1. The problem statement, all variables and given/known data

    factorise: [tex]a^3 + b^3 + c^3 - 3abc[/tex]

    2. Relevant equations

    3. The attempt at a solution

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

    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?

  2. jcsd
  3. Feb 6, 2008 #2
    I don't think you can. I stuck it into both maple and mathematica and they return the same factors as you have found.
  4. Feb 6, 2008 #3
    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.
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