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

Question

Докажите тождество!!


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

Answer 1

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