factorize (a+b)^3+(a-b)^3

圖片參考：http://codecogs.izyba.com/gif.latex?%28a+b%29%5E%7B3%7D+%28a-b%29%5E%7B3%7D%5C%5C%20=%28a+b+a-b%29%5B%28a+b%29%5E%7B2%7D-%28a+b%29%28a-b%29+%28a-b%29%5E%7B2%7D%5D%5C%5C%20=2a%28a%5E%7B2%7D+2ab+b%5E%7B2%7D-a%5E%7B2%7D+b%5E%7B2%7D+a%5E%7B2%7D-2ab+b%5E%7B2%7D%29%5C%5C%20=2a%28a%5E2+3b%5E2%29


希望幫到你,
其實你將(a+b)=c, (a-b)=d >>>c^3+d^3
咁你代返D a and b 落條式就得

(a+b)^3+(a-b)^3
=3(a+b)+3(a-b)
=3a+3b+3a-3b
=6a.

(a+b)^3+(a-b)^3
=(a^2+2ab+b^2)(a+b)+(a^2-2ab+b^2)(a-b)
=a^3+2a^2b+ab^2+ab^2+2ab^2+b^3+b^3+a^3-2a^2b+ab^2-a^2b+2ab^2-b^2
=2a^3+2ab^2+4ab^2