做几道数学题

题目

做几道数学题
(x+2y-7z)^3+(3x-4y+6z)^3-(4x-2y-z)^3

答案

设
x+2y-7z = a
3x-4y+6z= b
4x-2y-z = c
则a+b=c
a^3+b^-c^3
=(a+b)^-3a^2b-3ab^2 - c^3
=-3ab(a+b)
=-3abc
=-3(x+2y-7z)(3x-4y+6z)(x+2y-7z )