作业帮证明x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2能被x+y+z整除
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证明x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2能被x+y+z整除
证明x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2能被x+y+z整除
证明x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2能被x+y+z整除
证明：∵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)^2-4x^2y^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)
∴(x+y+z)是x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2的一个因式
∴x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2能被x+y+z整除
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