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

题目

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

答案

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
^_^