急！因式分解詳細步驟

👨🏻‍🏫 學術台數學

[匿名]

2014-10-06 3:33 am

1. x^2 - y^2 + 2x + 1

2. x^2 - y^2 - x + y

3. 2(a-b)^2 - a^2 + b^2

4. x+y 必為下列何者的因式
I. x^2 - y^2
II. x^2 + y^2
III. x (x + y) - x - y

5. x^2 - x - xy + y

6. pr + qr - ps - qs

7.ab + ac - a^2 - bc

8.(4x + y)^2 - (4x - y)^2

9.x^3 - 27/x^3

要詳細步驟急! 唔該哂

更新1:

其實我有答案但我唔識點計個答案出黎所以需要步驟不如我比埋個答案你因為見你有d題目計錯左麻煩你再計多一次 thx 答案如下: 1. (x + y +1)(x - y + 1) 2. (x - y)(x + y - 1) 3. a - 3b 4. 只有I 及 III 5. (x - y)(x - 1) 6. (p + q)(r - s) 7. (a - b)(c - a) 8. 16xy 9. (x - 3/x)(x^2 + 3 + 9/x^2)

回答 (2)

用戶7639

2014-10-06 10:18 am

✔ 最佳答案

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用戶88176

2014-10-06 3:57 am

1. x^2 - y^2 + 2x + 1
=(x+1)^2 -y^2
=(x+1-y)(x+1+y)

2. x^2 - y^2 - x + y
=(x-y)(x+y) - (x-y)
=(x-y)(x+y-1)

3. 2(a-b)^2 - a^2 + b^2
=2(a-b)^2 - (a^2 - b^2)
=2(a-b)^2 - [ (a-b)^2 + 2ab]
=(a-b)^2 + 2ab
=a^2 - b^2

4. x+y 必為下列何者的因式
I. x^2 - y^2 = (x-y)(x+y)
II. x^2 + y^2 = (x+y)(x+y) - 2ab
III. x (x + y) - x - y = x(x+y) - (x+y) = (x+y)(x-1)

Anx : I, II, III

5. x^2 - x - xy + y
=x(x-1) - (y)(x-1)
=(x-1)(x-y)

6. pr + qr - ps - qs
=p(r-s) + q(r-s)
=(r-s)(p+q)

7.ab + ac - a^2 - bc
=b(a-c)-a(a-c)
=(a-c)(b-a)

8.(4x + y)^2 - (4x - y)^2
=(4x+y-4x+y)(4x+y+4x-y)
=(2y)(8x)
=16xy

9.x^3 - 27/x^3
=x^3 - (3/x)^3
=[x-(3/x)][x^2+(x)(3/x)+(3/x)^2]
={[(x^2)-3] / x}[x^2+3+9/x^2]

2014-10-05 20:04:46 補充：
3. 2(a-b)^2 - a^2 + b^2
=2a^2 - 4ab + 2b^2 - a^2 + b^2
=a^2 - 4ab + 3b^2
=(a-b)(a-3b)

2014-10-05 20:07:26 補充：
9.x^3 - 27/x^3
=x^3 - (3/x)^3
=[x-(3/x)][x^2+(x)(3/x)+(3/x)^2]
={[(x^2)-3] / x}[x^2+3+9/x^2]
=(x^6 - 27) / x^3

參考: me, me, me

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收錄日期: 2021-04-23 20:46:27
原文連結 [永久失效]:
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急！因式分解 詳細步驟

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急！因式分解詳細步驟