求证(a-b)^3=a^3-3a^2b+3ab^2-b^3

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

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

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

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