Довести тотожность примера:(a-b+c)^2=a^2+b^2+c^2-2ab+2ac-2bc

Докажем тождество  (a – b + c)^2 = a^2 + b^2 + c^2 – 2 * a * b + 2 * a * c – 2 * b * c; 

((a – b) + c)^2 = a^2 + b^2 + c^2 – 2 * a * b + 2 * a * c – 2 * b * c;

(a – b)^2 + 2 * (a – b) * c + c^2 = a^2 + b^2 + c^2 – 2 * a * b + 2 * a * c – 2 * b * c;

a^2  - 2 * a * b + b^2 + 2 * a * c - 2 * b * c + c^2 = a^2 + b^2 + c^2 – 2 * a * b + 2 * a * c – 2 * b * c; 

a^2 + b^2 + c^2 – 2 * a * b + 2 * a * c – 2 * b * c = a^2 + b^2 + c^2 – 2 * a * b + 2 * a * c – 2 * b * c;

Верно.