因式分解 (x²+y²-1)²-4x²y²

问题描述:

因式分解 (x²+y²-1)²-4x²y²

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