证明：x四次方+y四次方+z四次方-2x平方y平方-2x平方z平方-2y平方z平方能被x+y+z整除.

分解因式：
x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2
= x^4+y^4+z^4+2x^2y^2-2x^2z^2-2y^2z^2-4x^2y^2
= (x^2+y^2-z^2)^2-(2xy)^2
= (x^2+y^2-z^2+2xy)(x^2+y^2-z^2-2xy)
= [(x+y)^2-z^2][(x-y)^2-z^2]
= (x+y+z)(x+y-z)(x-y+z)(x-y-z)
可得：
x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2 能被 x+y+z 整除.