因式分解 速回xy﹙xy+1﹚+﹙xy+3﹚-2﹙x+y+1/2﹚-﹙x+y-1﹚²
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因式分解 速回
xy﹙xy+1﹚+﹙xy+3﹚-2﹙x+y+1/2﹚-﹙x+y-1﹚²
xy﹙xy+1﹚+﹙xy+3﹚-2﹙x+y+1/2﹚-﹙x+y-1﹚²
![因式分解 速回xy﹙xy+1﹚+﹙xy+3﹚-2﹙x+y+1/2﹚-﹙x+y-1﹚²](/uploads/image/z/19873601-17-1.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3+%E9%80%9F%E5%9B%9Exy%EF%B9%99xy%EF%BC%8B1%EF%B9%9A%EF%BC%8B%EF%B9%99xy%EF%BC%8B3%EF%B9%9A%EF%BC%8D2%EF%B9%99x%EF%BC%8By%EF%BC%8B1%EF%BC%8F2%EF%B9%9A%EF%BC%8D%EF%B9%99x%EF%BC%8By%EF%BC%8D1%EF%B9%9A%26%23178%3B)
原式=x^2y^2+2xy-2x-2y+2-(x+y-1)^2
=x^2y^2+2xy-2(x+y-1)-(x+y-1)^2
=x^2y^2+2xy-[2(x+y-1)+(x+y-1)^2]
=x^2y^2+2xy-(x+y-1)(x+y+1)
=x^2y^2+2xy-(x+y)^2+1
=x^2y^2+2xy-(x^2+2xy+y^2)+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+2xy-2(x+y-1)-(x+y-1)^2
=x^2y^2+2xy-[2(x+y-1)+(x+y-1)^2]
=x^2y^2+2xy-(x+y-1)(x+y+1)
=x^2y^2+2xy-(x+y)^2+1
=x^2y^2+2xy-(x^2+2xy+y^2)+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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