神马作文网因式分解 速回xy﹙xy＋1﹚＋﹙xy＋3﹚－2﹙x＋y＋1／2﹚－﹙x＋y－1﹚²
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/18 17:58:56
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
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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