证明;x4+y4+z4-2x2y2-2x2y2-2y2z2能被(x+y+z)整除

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证明;x4+y4+z4-2x2y2-2x2y2-2y2z2能被(x+y+z)整除
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证明;x4+y4+z4-2x2y2-2x2y2-2y2z2能被(x+y+z)整除
证明;x4+y4+z4-2x2y2-2x2y2-2y2z2能被(x+y+z)整除

证明;x4+y4+z4-2x2y2-2x2y2-2y2z2能被(x+y+z)整除
LHS=x4+y4+z4-2x2y2z-2x2yz2
=4(x+y+z)-2(x+y+z)
=(4-2)(x+y+z)
=2(x+y+z)
RHS=(x+y+z)
THUS
LHS/RHS=2
^_^