把多项式(xy-1)²+(x+y-2)(x+y-2xy)分解因式
答案:2 悬赏:0
解决时间 2021-02-17 15:39
- 提问者网友:痞子房西
- 2021-02-17 10:19
把多项式(xy-1)²+(x+y-2)(x+y-2xy)分解因式
最佳答案
- 二级知识专家网友:专属的偏见
- 2021-02-17 11:34
(xy-1)²+(x+y-2)(x+y-2xy)
=x²y²-2xy+1+(x+y)²-2xy(x+y)-2(x+y)+4xy
=x²y²+2xy+1+(x+y)²-2xy(x+y)-2(x+y)
=(xy+1)²-2(xy+1)(x+y)+(x+y)²
=(xy+1-x-y)²
=[x(y-1)-(y-1)]²
=(x-1)²(y-1)²
=x²y²-2xy+1+(x+y)²-2xy(x+y)-2(x+y)+4xy
=x²y²+2xy+1+(x+y)²-2xy(x+y)-2(x+y)
=(xy+1)²-2(xy+1)(x+y)+(x+y)²
=(xy+1-x-y)²
=[x(y-1)-(y-1)]²
=(x-1)²(y-1)²
全部回答
- 1楼网友:陪伴是最长情的告白
- 2021-02-17 12:34
xy-1+x-y
=xy+x-y-1
=x(y+1)-(y+1)
=(y+1) (x-1)
=xy+x-y-1
=x(y+1)-(y+1)
=(y+1) (x-1)
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