why (a+b)(aa-ab+bb)=aaa+bbb

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Leo Lo

2007-12-02 7:37 pm

why (a+b)(a*a-ab+b*b)=a*a*a+b*b*b
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更新1:

and (a-b)(a*a+ab+b*b)=a*a*a-b*b*b if any one know please answer,pleaseeeeeeee!!!!!!!!!!!!!!!!!!!!!!!! 趕住考試!!!!!!!!!!!!!!!!!!!!!!!!

回答 (2)

Sandra

2007-12-02 8:10 pm

✔ 最佳答案

(a+b)(aa-ab+bb)
=(a+b)(a^2-ab+b^2)
=a(a^2-ab+b^2)+b(a^2-ab+b^2)
=a^3-a^2b+ab^2+a^2b-ab^2+b^3
=a^3+b^3
=a*a*a+b*b*b

(a-b)(aa+ab+bb)
=(a-b)(a^2+ab+b^2)
=a(a^2+ab+b^2)-b(a^2+ab+b^2)
=a^3+a^2b+ab^2-a^2b-ab^2-b^3
=a^3-b^3
=a*a*a-b*b*b

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[匿名]

2007-12-02 8:06 pm

(a+b)(a^2-ab+b^2)
=a^3 - (a^2)b + a(b^2) + b(a^2) - a(b^2) +b^3
=a^3 + b^3

ps a^3 =a*a*a

呢個其本上係公式可以背左佢

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