因式分解(1-x2)(1-y2)-4xy急需答案 请大家帮忙

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因式分解(1-x2)(1-y2)-4xy急需答案 请大家帮忙
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因式分解(1-x2)(1-y2)-4xy急需答案 请大家帮忙
因式分解(1-x2)(1-y2)-4xy
急需答案 请大家帮忙

因式分解(1-x2)(1-y2)-4xy急需答案 请大家帮忙
(1-x^2)(1-y^2)-4xy
=1-y^2-x^2+x^2y^2-4xy
=x^2y^2-4xy+1-(x^2+y^2)
=x^2y^2-2xy+1-(x^2+y^2+2xy)
=(xy-1)^2-(x+y)^2
=(xy-1+x+y)(xy-1-x-y)

(1-x^2)(1-y^2)-4xy
=1-y^2-x^2+x^2y^2-4xy
=x^2y^2-4xy+1-(x^2+y^2)
=x^2y^2-2xy+1-(x^2+y^2+2xy)
=(xy-1)^2-(x+y)^2
=(xy-1+x+y)(xy-1-x-y)