a^3+b^3+c^3-3abc
=(a+b)^3-3ab(a+b)+c^3-3abc
=(a+b)^3+c^3-3ab(a+b)-3abc
=(a+b+c)^3-3(a+b)*c*(a+bc)-3ab(a+b+c)
=(a+b+c)*[(a+b+c)^2-3ab]
=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)
下面展开合并同类项=(a-b+b-c)^3+3(a-b)(b-c)(a-b+b-c)+(c-a)^3
=(a-c)^3+3(a-b)(b-c)(a-c)-(a-c)^3
=3(a-b)(b-c)(a-c)