展開8條(a+b)^(1 to 8)－lgzrelv的部落格

標題:

展開8條(a+b)^(1 to 8)

發問:

1.(a+b) 2.(a+b) 3.(a+b)? 4.(a+b)? 5.(a+b)? 6.(a+b)? 7.(a+b)? 8.[(a-b)(a+b)] 更新: 1.(a+b)^2 2.(a+b)^3 更新 2: What's nCr 更新 3: very gd

最佳解答:

1) (a+b)^2 =(a+b)(a+b) =a^2+ab+ab+b^2 =a^2+2ab+b^2 2) (a+b)^3 =(a+b)^2(a+b) =(a^2+2ab+b^2)(a+b) =a^3+a^2b+2a^2b+2ab^2+ab^2+b^3 =a^3+3a^2b+3ab^2+b^3 3) (a+b)^4 =(a+b)^3(a+b) =(a^3+3a^2b+3ab^2+b^3)(a+b) =a^4+a^3b+3a^3b+3a^2b^2+3a^2b^2+3ab^3+ab^3+b^4 =a^4+4a^3b+6a^2b^2+4ab^3+b^4 4) (a+b)^5 =(a+b)^4(a+b) =(a^4+4a^3b+6a^2b^2+4ab^3+b^4)(a+b) =a^5+a^4b+4a^4b+4a^3b^2+6a^3b^2+6a^2b^3+4a^2b^3+4ab^4+ab^4+b^5 =a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5 5) (a+b)^6 =(a+b)^5(a+b) =(a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5)(a+b) =a^6+a^5b+5a^5b+5a^4b^2+10a^4b^2+10a^3b^3+10a^3b^3+10a^2b^4+5a^2b^4+5ab^5+ab^5+b^6 =a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6 6) (a+b)^7 =(a+b)^6(a+b) =(a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6)(a+b) =a^7+a^6b+6a^6b+6a^5b^2+15a^5b^2+15a^4b^3+20a^4b^3+20a^3b^4+15a^3b^4+15a^2b^5+6a^2b^5+6ab^6+ab^6+b^7 =a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7 7) (a+b)^8 =(a+b)^7(a+b) =(a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7)(a+b) =a^8+a^7b+7a^7b+7a^6b^2+21a^6b^2+21a^5b^3+35a^5b^3+35a^4b^4+35a^4b^4+35a^3b^5+21a^3b^5+21a^2b^6+7a^2b^6+7ab^7+ab^7+b^8 =a^8+8a^7b+28a^6b^2+56a^5b^3+70a^4b^4+56a^3b^5+28a^2b^6+8a^7b+a^8 8) (a-b)(a+b) =a^2+ab-ab-n^2 =a^2-b^2 2009-11-12 13:17:09 補充：不過如果你識得nCr就可輕鬆解答問題 2009-11-12 14:59:19 補充： nCr是n樣東西中抽r組合以(a+b)^3 =(a+b)(a+b)(a+b) 如果求a^2b的係數我要在3個括號抽2個抽號先會出現a^2b 即3C2=3 不過如你唔係中四m2或amaths或高考可以ignore