分解因式x4+y4+(x+y)4-2
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x4+y4+(x+y)4-2=（x2+y2）2-2x2y2+(x+y)4-2
=[(x+y)2-2xy]2-2x2y2+(x+y)4-2
=(x+y)4-4xy(x+y)2+4x2y2-2x2y2+(x+y)4-2
=2(x+y)4-4xy(x+y)2+2x2y2-2
=2[(x+y)4-2xy(x+y)2+x2y2]-2
=2[(x+y)2-xy]2-2
=2[x2+y2+xy]2-2=2(x2+y2+xy+1)(x2+y2+xy-1)
=[(x+y)2-2xy]2-2x2y2+(x+y)4-2
=(x+y)4-4xy(x+y)2+4x2y2-2x2y2+(x+y)4-2
=2(x+y)4-4xy(x+y)2+2x2y2-2
=2[(x+y)4-2xy(x+y)2+x2y2]-2
=2[(x+y)2-xy]2-2
=2[x2+y2+xy]2-2=2(x2+y2+xy+1)(x2+y2+xy-1)
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