Question

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

Answer 1

А=b=a^4-b^4; 2)(a^4+b^4)(a^2+b^2)(a+b)(a-b)=a^8-b^8

Answer 2

$1) (a-b)(a+b)(a^2+b^2)=a^4-b^4 \ (a^2-b^2)(a^2+b^2)=a^4-b^4 \ a^4-b^4=a^4-b^4$

$2) (a^4+b^4)(a^2+b^2)(a+b)(a-b)=a^8-b^8 \ (a^4+b^4)(a^2+b^2)(a^2-b^2)=a^8-b^8 \ (a^4+b^4)(a^4-b^4)=a^8-b^8 \ a^8-b^8=a^8-b^8$