(a+b)^5-(a-b)^5=?
回答 (4)
2006-10-14 5:53 pm
✔ 最佳答案
(a+b)5-(a-b)5=?=a5+5a4b+10a3b2+10a2b3+5ab4+b5 – (a5-5a4b+10a3b2-10a2b3+5ab4-b5)
=a5+5a4b+10a3b2+10a2b3+5ab4+b5 – a5+5a4b-10a3b2+10a2b3-5ab4+b5
=10a4b+20a2b3+2b5
= 2b(5a4 + 10a2b2 + b4)
2006-10-14 6:44 pm
其實有個方法係快D可以計到的..................
(a+b)^5-(a-b)^5
= [ (a)^5+2(a)(b)+(b)^5 ] - [ (a)^5-2(a)(b)+(b)^5 ]
= a^5+2ab+b^5 - a^5-2ab+b^5
= a^5- a^5+b^5+b^5+2ab -2ab
= 2b^5
(a+b)^5-(a-b)^5
= [ (a)^5+2(a)(b)+(b)^5 ] - [ (a)^5-2(a)(b)+(b)^5 ]
= a^5+2ab+b^5 - a^5-2ab+b^5
= a^5- a^5+b^5+b^5+2ab -2ab
= 2b^5
2006-10-14 6:03 pm
用列表做 :
(a+b)^5-(a-b)^5=?
a^ 5a^4b a^3b^2 a^2b^3 ab^4 b^5
+1 +5 +10 +10 +5 +1
-1 +5 -10 +10 -5 +1
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
0 +10 +0 +20 +0 +2
(a+b)^5-(a-b)^5
= 10+a^4b+20a^2b^3+2b^5
(a+b)^5-(a-b)^5=?
a^ 5a^4b a^3b^2 a^2b^3 ab^4 b^5
+1 +5 +10 +10 +5 +1
-1 +5 -10 +10 -5 +1
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
0 +10 +0 +20 +0 +2
(a+b)^5-(a-b)^5
= 10+a^4b+20a^2b^3+2b^5
2006-10-14 5:56 pm
Make use of X^5 - Y^5 = (X-Y)(X^4 + X^3Y + X2Y^2 + XY^3 + Y^4)
(a+b)^5-(a-b)^5
=((a+b)-(a-b))((a+b)^4 + (a+b)^3(a-b) + (a+b)^2(a-b)^2 + (a+b)(a-b)^3 + (a-b)^4)
=2b((a+b)^4 + (a+b)^3(a-b) + (a+b)^2(a-b)^2 + (a+b)(a-b)^3 + (a-b)^4)
(a+b)^5-(a-b)^5
=((a+b)-(a-b))((a+b)^4 + (a+b)^3(a-b) + (a+b)^2(a-b)^2 + (a+b)(a-b)^3 + (a-b)^4)
=2b((a+b)^4 + (a+b)^3(a-b) + (a+b)^2(a-b)^2 + (a+b)(a-b)^3 + (a-b)^4)
收錄日期: 2021-04-12 22:56:59
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061014000051KK00984