(a+1)(a-1)(a^2-a+1)(a^2+a+1)(a^6+1)(a^12+1)(a^24+1 - вопрос №868095311212161121241 от ryazhechkina 13.06.2022 15:36

Question

Алгебра: (a+1)(a-1)(a^2-a+1)(a^2+a+1)(a^6+1)(a^12+1)(a^24+1

ryazhechkina · Answer

(a+1)(a-1)(a^2-a+1)(a^2+a+1)(a^6+1)(a^12+1)(a^24+1)=
=(a^2-1)((a^2+1)^2-a^2)(a^6+1)(a^12+1)(a^24+1)=
=(a^2-1)(a^4+2a^2+1-a^2)(a^6+1)(a^12+1)(a^24+1)=
=(a^2-1)(a^4+a+1)(a^6+1)(a^12+1)(a^24+1)=
=(a^6-1)(a^6+1)(a^12+1)(a^24+1)=
=(a^12-1)(a^12+1)(a^24+1)=
=(a^24-1)(a^24+1)=a^48-1