Question

Треба довести тотожність .

Answer 1

${\underbrace{(a^2+b^2)(a^4-a^2b^2+b^4)}_{(a+b)(a^2-ab+b^2)=a^3+b^3}}-{\underbrace{(a^3-b^3)(a^3+b^3)}_{(a-b)(a+b)=a^2-b^2}}=a^6+b^6-(a^6-b^6)=\\\\\\a^6+b^6-a^6+b^6=2b^6$