Докажите тождество:(a-2b)^3-(a+b)^2(a-8b)=27ab^2

Question

Докажите тождество:
(a-2b)^3-(a+b)^2(a-8b)=27ab^2

Answer 1

=a^3 - 6a^2b + 12ab^2 - 8b^3 - (a^2+2ab+b^2)(a-8b)=
=a^3 -6 a^2b +12ab^2 - 8b^3 -a^3 + 8a^2b- -2a^2b+16ab^2-ab^2 +8b^3= 27 ab^2;
27ab^2 = 27ab^2