因式分解問題 (5分)

👨🏻‍🏫 學術台數學

Pakco Leung

2006-10-28 7:55 pm

因式分解
(x^2-y^2)+7(x^2+2xy+y^2)

更新1:

(x-1)^2-5(x-1)-24

更新2:

展開(7-a)(a^2+7a+49)

更新3:

-16s^2+24s-9

回答 (4)

Po Yee

2006-10-28 8:04 pm

✔ 最佳答案

(x^2-y^2)+7(x^2+2xy+y^2)
= x^2 - y^2 + 7x^2 + 14xy + 7y^2
= 8x^2 + 14xy +6y^2
= 2(4x^2 + 7xy +3y^2)
= 2(4x+3y)(x+y)

2006-10-28 12:08:43 補充：
會有個更快的方法:(x^2-y^2)+7(x^2+2xy+y^2) = (x+y)(x-y) + 7(x+y)^2= (x+y) [x-y+ 7(x+y)]= (x+y)(x-y+7x+7y)= (x+y)(8x+6y)= 2(x+y)(4x+3y)

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Anthony Fung

2006-10-28 8:22 pm

(x^2-y^2)+7(x^2+2xy+y^2)
= x^2 - y^2 + 7x^2 + 14xy + 7y^2
= 8x^2 + 14xy +6y^2
= 2(4x^2 + 7xy +3y^2)
= 2(4x+3y)(x+y)
會有個更快的方法:
(x^2-y^2)+7(x^2+2xy+y^2)
= (x+y)(x-y) + 7(x+y)^2
= (x+y) [x-y+ 7(x+y)]
= (x+y)(x-y+7x+7y)
= (x+y)(8x+6y)
= 2(x+y)(4x+3y)

希望幫到你求你選我最佳答案

求下你

唔該!!!!!!

唔該!!!!!!

參考: me

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火車頭

2006-10-28 8:08 pm

Ans:
Method 1:

= x^2 - y^2 + 7x^2 + 14xy + 7y^2

= 8x^2 + 14xy + 6y^2

= 2(4x^2 + 7xy + 3y^2)

= 2(x + y) (4x + 3y)

Method 2:

= (x + y)(x - y) + 7(x + y)^2

= (x + y) [(x - y) + 7(x + y)]

= (x + y) (x - y + 7x + 7y)

= (x + y) (8x + 6y)

= 2 (x + y) (4x + 3y)

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錦達

2006-10-28 8:04 pm

(x^2-y^2)+7(x^2+2xy+y^2)
=x^2-^2+7x^2+14xy+7y^2
=8x^2+14xy+6x^2
=(8x+6y)(x+y)
=做完

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收錄日期: 2021-04-29 23:52:32
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