Question

Упростите выражения :
(3m-n)^3-(n+3m)^3=
(a-b)^3+3ab (a-b)=
3ab(a+b)-(a+b)^3=
Пожалуйста помогите срочно
( ^ -степень)

Answer 1

$\displaystyle \tt (3m-n)^3-(n+3m)^3=27m^3-27m^2n+9mn^2-n^3-(n^3+9mn^2+27m^2n+27m^3)=27m^3-27m^2n+9mn^2-n^3-n^3-9mn^2-27m^2n-27m^3=-54m^2n-2n^3$

$\displaystyle \tt (a-b)^3+3ab(a-b)=a^3-3a^2b+3ab^2-b^3+3a^2b-3ab^2=a^3-b^3$

$\displaystyle \tt 3ab(a+b)-(a+b)^3=3a^2b+3ab^2-(a^3+3a^2b+3ab^2+b^3)=3a^2b+3ab^2-a^3-3a^2b-3ab^2-b^3=-a^3-b^3$