x+y+z=3m(m-x)^3+(m-y)^3+(m-z)^3-3(x-m)(y-m)(z-m)=?

Question

x+y+z=3m (m-x)^3+(m-y)^3+(m-z)^3-3(x-m)(y-m)(z-m)=?

Answer 1

(m-x)+(m-y)+(m-z)=0
令m-x,m-y,m-z分别是a,b,c
a+b+c=0
原式=a^3+b^3+c^3-3abc
=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)
=0