因式分解速回xy﹙xy＋1﹚＋﹙xy＋3﹚－2﹙x＋y＋1／2﹚－﹙x＋y－1﹚²

Question

因式分解 速回
xy﹙xy＋1﹚＋﹙xy＋3﹚－2﹙x＋y＋1／2﹚－﹙x＋y－1﹚²

Answer 1

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)