Докажите тождество (a-8)^2+2(a-8)(3-a)+(a-3)^2=25

Question

Докажите тождество
(a-8)^2+2(a-8)(3-a)+(a-3)^2=25

Answer 1

= a² - 16a + 64 - 2a² + 6a + 16a - 48 + a² - 6a + 9 = 64 - 48 + 9 = 25

Answer 2

=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