Question

Докажите равенство. (a-b)^3=a^3-3a^2b+3ab^2-b^3

Answer 1

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