因式分解x^2y^2-x^2-y^2+1

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因式分解x^2y^2-x^2-y^2+1

x^2y^2-x^2-y^2+1
=(x^2y^2-2xy+1)-(x^2-2xy+y^2)
=(xy-1)^2-(x-y)^2
=(xy-x+y-1)(xy+x-y-1)

(x-1)(x+1)(y-1)(y+1)

x^2y^2-x^2-y^2+1
=x^2(y^2-1)-(y^2-1)
=(x^2-1)(y^2-1)
=(x+1)(x-1)(y+1)(y-1)

x^2y^2-x^2-y^2+1
=x^2(y^2-1)-(y^2-1)
=(x^2-1)(y^2-1)
=(x+1)(x-1)(y+1)(y-1)

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