(x+y+z)(x-y+z)(x+y-z)(-x+y+z)

2026年09月25日 11:36

有2个网友回答

网友（1）：

原式=[(x+z)+y][(x+z)-y][y+(x-z)][y-(x-z)]
=[(x+z)²-y²][y²-(x-z)²]
=(x²+2xz+z²-y²)(y²-x²+2xz-z²)
=[2xz+(x²-y²+z²)][2xz-(x²-y²+z²)]
=4x²z²-(x^4+y^4+z^4-2x²y²+2x²z²-2y²z²)
=-x^4-y^4-z^4+2x²y²+2x²z²+2y²z²

网友（2）：

令a=x2+x
原式=(a+3)(a-1)-5
=a2+2a-3-5
=a2+2a-8
=(a+4)(a-2)
=(x2+x+4)(x2+x-2)
=(x2+x+4)(x+2)(x-1)