因式分解:(x²+y²-z²)²-4x²y²

来源：学生作业帮助网编辑：作业帮时间：2024/05/02 13:11:59

因式分解:(x²+y²-z²)²-4x²y²
因式分解:(x²+y²-z²)²-4x²y²

因式分解:(x²+y²-z²)²-4x²y²
(x²+y²-z²)²-4x²y²
=（x²+y²-z²+2xy)(x²+y²-z²-2xy)
=[(x+y)²-z²][(x-y)²-z²]
=(x+y+z)(x+y-z)(x-y+z)(x-y-z)

(x²+y²-z²)²-4x²y²
=(x²+y²-z²)²-(2xy)²
=[(x²+y²-z²)+2xy][(x²+y²-z²)-2xy]
=[(x+y)²-z²][(x-y)²-z²]
=(x+y-z)(x+y+z)(x-y+z)(x-y-z)