分解因式：（x²+y²-1）²-4x²y²

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 04:01:43

分解因式：（x²+y²-1）²-4x²y²
分解因式：（x²+y²-1）²-4x²y²

分解因式：（x²+y²-1）²-4x²y²
：（x²+y²-1）²-4x²y²
=（x²+y²-1+2xy)(x²+y²-1-2xy)
=[(x+y)²-1][(x-y)²-1]
=(x+y+1)(x+y-1)(x-y+1)(x-y-1)

(x²+y²-1)²-4x²y²
=(x²+y²-1)²-(2xy)²
=(x²+y²-1+2xy)(x²+y²-1-2xy)
=[(x+y)²-1][(x-y)²-1]
=(x+y+1)(x+y-1)(x-y+1)(x-y-1)