有些數學問題,,, 解難 @ bgdwze3的部落格

標題:

有些數學問題,,, 解難

發問:

(a-b)(b+a)(b-a)=? (a+b)(b+a)(b-a)=? 請例步驟.... thx thx/...

最佳解答:

1. (a-b)(b+a)(b-a) =(a+b)(a-b)(b-a) =(a2-b2)(b-a) =(a2-b2)(b)-(a2-b2)(a) =a2b-b3-a3+ab2 =a2b+ab2-b3-a3 * a2 b2 b3 is square and cube 2008-09-07 18:35:41 補充： 2. (a+b)(b+a)(b-a) =(a+b)(a+b)(b-a) =(a+b)2(b-a) =(a2+2ab+b2)(b-a) =(a2+2ab+b2)(b)-(a2+2ab+b2)(a) =a2b+2ab2+b3-a3+2a2b+ab2 =3a2b+3ab2-a3+b3 * a2 b2 (a+b)2 b3 is square and cube 2008-09-07 18:37:55 補充： The number "2" behind a number is also square e.g. 2a2b = 2 x a2 x b 3a2b = 3 x a2 x b 2008-09-07 18:44:01 補充： Some fomula inside the solution or for additional information 1.(a+b)(a-b) = (a2-b2) 2.(a+b)(a+b) [ (a+b)2 ] = (a2+2ab+b2) 3.(a-b)(a-b) [ (a-b)2 ] = (a2-2ab+b2) 4.(a2-b2) is not equal to (a-b)2 (a2+b2) is not equal to (a+b)2 2008-09-07 18:54:30 補充： The above fomula may be taught when you're form 1 or 2. b2 = b x b Prove: 1.(a+b)(a-b) = (a+b)(a)-(a+b)(b) = a2+ab-ab-b2 = a2-b2 2.(a+b)(a+b) = (a+b)(a)+(a+b)(b) = a2+ab+ab+b2 = a2+2ab+b2 3.(a-b)(a-b) = (a-b)(a)-(a-b)(b) = a2-ab-ab+b2 = a2-2ab+b2

其他解答:

我想知究竟您想將果2條式expand(擴分)定係factorize(分解)? 如果係expand就係呢個答案: 1.(a-b)(b+a)(b-a) =(a^2-b^2)(b-a)<---先拆頭２個括號及約簡(我己經約左) =a^2b-a^3-b^3+ab^2<---再拆第3個括號 =-a^3-b^3+a^2b+ab^2<----順序排例就係答案 2.(a+b)(b+a)(b-a) =(a^2+b^2+2ab)(b-a)<---同上面一樣 =a^2b-a^3+b^3-ab^2+2ab^2-2a^2b =-a^3+b^3+ab^2-a^2b fatorize就如下: 1.(a-b)(b+a)(b-a) =(a+b+1)(a-b)<----條式有2個(a-b),所以可以再約,就得出呢個答案 2.(a+b)(b+a)(b-a) =(-a+b+1)(a+b)<----同上希望幫到你吧~