求证(x+y+z)^3xyz-(yz+xz+xy)^3=xyz(x^3+y^3+z^3)-(y^3z^3+x^3z^3+x^3y^3)
问题描述：
求证(x+y+z)^3xyz-(yz+xz+xy)^3=xyz(x^3+y^3+z^3)-(y^3z^3+x^3z^3+x^3y^3)
答
证明:（x+y+z)^3xyz-xyz(x^3+y^3+z^3)＝xyz((x+y+z)^3-(x^3+y^3+z^3))=xyz(3xy^2+3xz^2+3x^2y+3Y^2z+3yz^2+3x^2z)=3xyz(xy^2+xz^2+x^2y+y^2z+yz^2+x^2z)令xy=a,yz=b,zx=c,并代入上式,得（x+y+z)^3xyz-xyz(x^3+y^3+z^...