作业帮分解因式(2X²-3X+1)²-22X²+33X-1 （x+y-2XY)(x+y-2)+(
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/09 09:31:21
分解因式(2X²-3X+1)²-22X²+33X-1 （x+y-2XY)(x+y-2)+(xy-1)^2
a=2x²-3x+1
11a=22x²-33x+11
所以原式=a²-11a+10
=(a-1)(a-10)
=(2x²-3x+1-1)(2x²-3x+1-10)
=x(2x-3)(2x+3)(x-3)
（x+y-2XY)(x+y-2)+(xy-1)^2
=[（x+y)-2xy][(x+y)-2]+(xy-1)²
=(x+y)²-2(xy+1)(x+y)+4xy+x²y²-2xy+1
=(x+y)²-2(xy+1)(x+y)+x²y²+2xy+1
=(x+y)²-2(xy+1)(x+y)+(xy+1)²
=[(x+y)-(xy+1)]²
=(x+y-xy-1)²
=[x(1-y)-(1-y)]²
=(x-1)²(1-y)²
=(x-1)²(y-1)²
11a=22x²-33x+11
所以原式=a²-11a+10
=(a-1)(a-10)
=(2x²-3x+1-1)(2x²-3x+1-10)
=x(2x-3)(2x+3)(x-3)
（x+y-2XY)(x+y-2)+(xy-1)^2
=[（x+y)-2xy][(x+y)-2]+(xy-1)²
=(x+y)²-2(xy+1)(x+y)+4xy+x²y²-2xy+1
=(x+y)²-2(xy+1)(x+y)+x²y²+2xy+1
=(x+y)²-2(xy+1)(x+y)+(xy+1)²
=[(x+y)-(xy+1)]²
=(x+y-xy-1)²
=[x(1-y)-(1-y)]²
=(x-1)²(1-y)²
=(x-1)²(y-1)²
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