(X-Y)3+(Y-Z)3+(Z-X)3 因式分解
问题描述：
(X-Y)3+(Y-Z)3+(Z-X)3 因式分解
答
原式 = X^3 - 3X^2 *Y + 3X*Y^2 - Y^3 + Y^3 - 3Y^2 *Z + 3Y*Z^2 - Z^3
+ Z^3 - 3Z^2 *X + 3Z*X^2 - X^3
= 3X*Y^2 - 3X^2 *Y + 3Y*Z^2 - 3Y^2 *Z + 3Z*X^2 - 3Z^2 *X
答
(x-y)^3+(y-z)^3+(z-x)^3
=[(x-y)^3+(y-z)^3]+(z-x)^3
=(x-y+y-z)[(x-y)^2-(x-y)(y-z)+(y-z)^2]+(z-x)^3
=(x-z)(3y^2-3xy+3xz-3yz)
=3(x-z)(x-y)(z-y)