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標題:

Factorize a^3 + b^3. (with steps,NOT identity only)

發問:

Factorize a^3 + b^3. (f.2 MATH) 上年考試題目(4分)，我知ans，但show不到step，得1分 請高人指教！ 更新: why the first step can change a^3 + b^3 to =(a+b)^3 - 3a^2b - 3ab^2?

最佳解答:

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此文章來自奇摩知識+如有不便請留言告知

a^3 + b^3 =(a+b)^3 - 3a^2b - 3ab^2 =(a+b)^3 - 3ab(a+b) =(a+b)[(a+b)^2 - 3ab] =(a+b)(a^2+2ab+b^2 - 3ab) =(a+b)(a^2-ab+b^2) //

其他解答:

(a+b)^3 - 3a^2b - 3ab^2?? (a+b)^3 = a^3 +3a^2b + 3ab^2 + b^3 as you are going to factorize a^3 + b^3 so you have to delete back 3a^2b + 3ab^2