(a+b)^5-(a-b)^5=- @ udd18ql48m的部落格

標題:

(a+b)^5-(a-b)^5=?

發問:

(a+b)^5-(a-b)^5=?

最佳解答:

(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)

其他解答:

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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|||||用列表做 : (a+b)^5-(a-b)^5=? a^5a^4ba^3b^2a^2b^3ab^4b^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|||||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)