Question

what are the factors of a²⁴+1? ​

Answer 1

a^24 +1

= (a^8)³ + 1

by using formula

a³ +b³ = (a+b) ( a²+b²-ab)

(a^8)³+1³ = (a^8 +1)(a^16 +1-a^8)

= [(a^4)² +1²](a^16+1-a^8)

by using formula a²+b² = (a+b)²-2ab

= [ (a^4+1)²-2a^4](a^16+1-a^8)

= (a^4+1-√2a²)(a^4+1+√2a²)(a^16+1-a^8)

it is by using x²-y² = (x+y)(x-y)

where x= a^4+1 and y = √2a²

i hope it will help u