证明：x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2
热心网友
是分解因式呗！ x^4 + y^4 + z^4 - 2x^2y^2 - 2x^2z^2 - 2y^2z^2= (x^4+2x^2y^2+y^4) + z^4 - 2x^2z^2 - 2y^2z^2 - 4x^2y^2= (x^2 + y^2)^2 - 2z^2(x^2+y^2) + z^4 - 4x^2y^2= (x^2 + y^2 - z^2)^2 - 4x^2y^2= (x^2 + y^2 - z^2 + 2xy) (x^2 + y^2 - z^2 - 2xy)= [ (x + y)^2 - z^2 ] [ (x - y)^2 - z^2 ]= (x + y + z)(x + y - z)(x - y + z)(x - y - z)
热心网友
没看懂！！
热心网友
证明什么？