分解因式:（1） (x-y)³-(x-y) （2）x³y³-2x²y²+xy （3）a³c-4a²bc+4ab²c （4）（x²+y²）²-4x²y²
急啊！
分解因式:（1） (x-y)³-(x-y) （2）x³y³-2x²y²+xy
答案:4 悬赏:0 手机版
解决时间 2021-02-08 02:01
- 提问者网友：末路
- 2021-02-07 06:40
最佳答案
- 五星知识达人网友：人间朝暮
- 2021-02-07 06:58
1x²y³－2x²y²＋xy =xy(xy²-2xy+1)
2 a﹙x-y﹚-b﹙y－x﹚＋c﹙x－y﹚=a﹙x-y﹚+b﹙x-y﹚＋c﹙x－y﹚=(a+b+c)(x-y)
[﹙x－y﹚²＋﹙x＋y﹚﹙x－y﹚]÷2x,=(x^2-2xy+y^2+x^2-y^2)\2x=(2x^2-2xy)\2x=x-y=3-15=-12
全部回答
- 1楼网友：爱难随人意
- 2021-02-07 11:00
(x-y)³-(x-y)
=(x-y) {(x-y)²-1}
=(x-y)(x-y-1)(x-y+1）
x³y³-2x²y²+xy
=xy(x²y²-2xy+1)
=xy(xy-1)²
a³c-4a²bc+4ab²c
=ac(a²-4ab+4b²)
=ac(a-2b)²
（x²+y²）²-4x²y²
=x^4+2x²y²+y^4-4x²y²
=x^4-2x²y²+y^4
=(x²-y²)²
=(x+y)²(x-y)²
- 2楼网友：毛毛
- 2021-02-07 09:32
（1） (x-y)³-(x-y)
＝(x-y)[(x-y)²-1]
=(x-y)(x-y+1)(x-y-1)
（2）x³y³-2x²y²+xy
=xy(x²y²-2xy+1)
=xy(xy-1)²
（3）a³c-4a²bc+4ab²c
=ac(a²-4ab+4b²)
=ac(a-2b)²
（4）（x²+y²）²-4x²y²
=(x²+y²+2xy)(x²+y²-2xy)
=(x+y)²(x-y)²
- 3楼网友：封刀令
- 2021-02-07 08:00
(x-y)³-(x-y)=(x-y)(x²+y²-2xy-1)
x³y³-2x²y²+xy =xy(x²y²-2xy+1)=xy(xy-1)²
a³c-4a²bc+4ab²c=ac(a²-4ab+4b²)=ac(a-4b)²
(x²+y²）²-4x²y² =(x²+y²+2xy)(x²-2xy+y²)=(x+y)²(x-y)²
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