因式分解(2) 送分

👨🏻‍🏫 學術台數學

Ray

2009-01-16 1:12 am

1. xy(x-y)+3y(y-x)
2. 2x(x-3y)+x(3y-x)
3. 4xy(3y-x)-2x(x-3y)
4. (x-y)-x+y=
5. 2x(y-z)-4z+4yz
6. 3x(x-2y)+9xy(2y-x)
7. 6xy(3y-x)-3x(x-3y)

更新1:

之前果條禁錯制del左,唔好意思

更新2:

改一改題目 1. xy(x-y)+3y(y-x)^2 2. 2x^2(x-3y)+x(3y-x)^2 3. 4xy^2(3y-x)-2x^2(x-3y)^2 4. (x-y)^2-x+y= 5. 2x(y-z)-4z^2+4yz 6. 3x^2(x-2y)+9xy^2(2y-x) 7. 6xy^2(3y-x)-3x^2(x-3y)^2

回答 (3)

老爺子

2009-01-16 1:48 am

✔ 最佳答案

1.
xy(x - y) + 3y(y - x)2
= xy(x - y) + 3y(x - y)2
= y(x - y)[x + 3(x - y)]
= y(x - y)(4x - 3y)

2.
2x2(x - 3y) + x(3y - x)2
= 2x2(x - 3y) + x(x - 3y)2
= x(x - 3y)[2x + (x - 3y)]
= x(x - 3y)(3x - 3y)
= 3x(x - 3y)(x - y)

3.
4xy2(3y - x) - 2x2(x - 3y)2
= 4xy2(3y - x) - 2x2(3y - x)2
= 2x(3y - x)[2y2 - x(3y - x)]
= 2x(3y - x)(2y2 - 3xy + x2)
= 2x(3y - x)(2y - x)(y - x)

4.
(x - y)2 - x + y
= (x - y)2 - (x - y)
= (x - y)[(x - y) -1]
= (x - y)(x - y - 1)

5.
2x(y - z) - 4z2 + 4yz
= 2x(y - z) + 4z(y - z)
= (2x + 4z)(y - z)
= 2(x + 2z)(y - z)

6.
3x2(x - 2y) + 9xy2(2y - x)
= 3x2(x - 2y) - 9xy2(x - 2y)
= (3x2 - 9xy2)(x - 2y)
= 3x(x - 3y2)(x - 2y)

7.
6xy2(3y - x) - 3x2(x - 3y)2
= 6xy2(3y - x) - 3x2(3y - x)2
= 3x(3y - x)[2y2 - x(3y - x)]
= 3x(3y - x)[2y2 - 3xy + x2]
= 3x(3y - x)(2y - x)(y - x)
=

👍 0 👎 0

[匿名]

2009-01-16 2:16 am

答案: 1.xy(x - y) + 3y(y - x)2
= xy(x - y) + 3y(x - y)2
= y(x - y)[x + 3(x - y)]
= y(x - y)(4x - 3y)

2.
2x2(x - 3y) + x(3y - x)2
= 2x2(x - 3y) + x(x - 3y)2
= x(x - 3y)[2x + (x - 3y)]
= x(x - 3y)(3x - 3y)
= 3x(x - 3y)(x - y)

3.
4xy2(3y - x) - 2x2(x - 3y)2
= 4xy2(3y - x) - 2x2(3y - x)2
= 2x(3y - x)[2y2 - x(3y - x)]
= 2x(3y - x)(2y2 - 3xy + x2)
= 2x(3y - x)(2y - x)(y - x)

4.
(x - y)2 - x + y
= (x - y)2 - (x - y)
= (x - y)[(x - y) -1]
= (x - y)(x - y - 1)

5.
2x(y - z) - 4z2 + 4yz
= 2x(y - z) + 4z(y - z)
= (2x + 4z)(y - z)
= 2(x + 2z)(y - z)

6.
3x2(x - 2y) + 9xy2(2y - x)
= 3x2(x - 2y) - 9xy2(x - 2y)
= (3x2 - 9xy2)(x - 2y)
= 3x(x - 3y2)(x - 2y)

7.
6xy2(3y - x) - 3x2(x - 3y)2
= 6xy2(3y - x) - 3x2(3y - x)2
= 3x(3y - x)[2y2 - x(3y - x)]
= 3x(3y - x)[2y2 - 3xy + x2]
= 3x(3y - x)(2y - x)(y - x)

👍 0 👎 0

[匿名]

2009-01-16 1:20 am

功課問老師吧啦@@
一係打電話問同學都得!

👍 0 👎 0

收錄日期: 2021-04-29 18:14:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090115000051KK01031

檢視 Wayback Machine 備份