Question

Помогите доказать тождество
(b+c-2a)(c-b)+(c+a-2b)(a-c)-(a+b-2c)(a-b)=0

Answer 1

(b+c-2a)(c-b)+(c+a-2b)(a-c)-(a+b-2c)(a-b)=
=bc+c²-2ac-b²-bc+2ab+ac+a²-2ab-c²-ac+2bc-a²-ab+2ac+ab+b²-2bc=
=(bc-bc+2bc-2bc)+(ac-ac+2ac-2ac)+(ab-ab+2ab-2ab)+(a²-a²+b²-b²+c²-c²)≡0.