x^4+y^4+z^4+1+8xyz-2(y^2z^2+z^2x^2+x^2y^2+x^2+y^2+z^2）
=（x^2+y^2)+(z^2+1)^2+8xyz-4x^2y^2-2x^2z^2-2y^2z^2-2x^2-2y^2-4z^2
=（x^2+y^2)+(z^2+1)^2+8xyz-2z^2(x^2+y^2)-2(x^2+y^2)-4x^2y^2-4z^2
=（x^2+y^2)+(z^2+1)^2-2(z^2+1)(x^2+y^2)+4(2xyz-x^2y^2-z^2)
=[(x^2+y^2)-(z^2+1)]^2-[2(xy-z)]^2
=(x^2+y^2-z^2-1+2xy-2z)(x^2+y^2-z^2-1-2xy+2z)