设Ax=a,By=b,Cz=c 则原式化为：(a-b)^3+(b-c)^3-(a-c)^3=(a-b+b-c)[(a-b)^2-(a-b)(b-c)+(b-c)^2]-(a-c)^3=(a-c)[(a-b)^2-(a-b)(b-c)+(b-c)^2]-(a-c)^3=(a-c)[(a-b)^2-(a-b)(b-c)+(b-c)^2-(a-c)^2]=(a-c)[(a-b)(a-b-b+c)+(b-c+a-c)(b-c-a+c)]=(a-c)[(a-b)(a-2b+c)+(a+b-2c)(b-a)]=(a-c)(a-b)(a-2b+c-a-b+2c)=(a-c)(a-b)(-3b+3c)=-3*(a-c)(a-b)(b-c)= -3(Ax-By)(Ax-Cz)(By-Cz)