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定理:p(x)=x^n+a(n-1)x^(n-1)+..+a0,
则p(x)=(x-b1)(x-b2)..(x-bn),其中b1,b2,..,bn为
p(x)的根.

1.
x^3-3xy+y^3+1=
=(x+y)(x^2-xy+y^2)-3xy+1=
=(x+y+1)(x^2-xy+y^2)-[x^2+2xy+y^2-1]=
=(x+y+1)(x^2-xy+y^2)-[(x+y)^2-1]=
=(x+y+1)(x^2-xy+y^2-x-y+1)=
=(x+y+1)[(x-y)^2+(x-1)^2+(y-1)^2]/2

2.:p(Z)=Z^6-1,的6个根为:e^(2kπi/6),k=0,1,2,3,4,5.
根据定理得:
Z^6-1=
=(Z-1)(Z-e^(πi/3))(Z-e^(2πi/3))*
*(Z-e^(πi))(Z-e^(4πi/3))(Z-e^(5πi/3))

==>
x^6-y^6=y^6[(x/y)^6-1]=
=(x-y)(x-e^(πi/3)y)(x-e^(2πi/3)y)*
*(x-e^(πi)y)(x-e^(4πi/3)y)(x-e^(5πi/3)y).