Question

Докажите тождество: 1) (а-b)(a+b)(a^2+b^2)=a^4-b^4 2) (а^4+b^4)(a^2+b^2)(a+b)(a-b)=a^8-b^8

Answer 1

1. (a^2-b^2)(a^2+b^2)=a^2*a^2+a^2*b^2-a^2*b^2-b^2*b^2= a^4-b^4
2. (a^4+b^4)(a^4-b^4)=a^8+a^4*b^4-a^4*b^4-b^8=a^8-b^8