Докажите тождество (x-1)(x+1)(x^2+1)(x^4+1)=x^8-1

Question

Докажите тождество (x-1)(x+1)(x^2+1)(x^4+1)=x^8-1

Answer 1

(x-1)(x+1)(x^2+1)(x^4+1)=x^8-1
(x^2-1)(x^2+1)(x^4+1)=x^8-1
(x^4-1)(x^4+1)=x^8-1
x^8-1=x^8-1