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

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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:

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
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