How would I factor $a^3+b^3+c^3-6abc$ How would I factor the polynomial $a^3+b^3+c^3-6abc$? The values are homogenous, so so must be the factors. I don't know where to go from there.

$$a^3+b^3+c^3-6abc= (a+b)^3-3ab(a+b)+c^3-6abc
\\(a+b+c)^3-3(a+b)c(a+b+c) -3ab(a+b)-6abc
\\=(a+b+c)^3 -3(a+b)c(a+b+c)-3ab(a+b)-(3+3)abc
\\=(a+b+c)^3-3c((a+b)(a+b+c)) -3ab(a+b+c) $$
now factor $$ (a+b+c) $$ and go on
$$(a+b+c)((a+b+c)^2 -3c(a+b) -3ab) )
\\=(a+b+c)(a^2+b^2+c^2+2ab+2ac+2bc-3ab-3bc-3ac)
\\=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)
$$
