Question

a^4/4 +4/a^4 +1factorise..+1 is not included 4a^4

Answer 1

so we have (a^4/4) + (4/a^4) + 1

= (a^8 + 16 + 4a^4)/(4a^4)
= a^8 + 8a^4 + 16 + 4a^4 - 8a^4)/(4a^4) <---- completing the square
= ( (a^4 + 4)^2 - 4a^4)/(4a^4)
= (a^4 + 4 + 2a^2)(a^4 + 4 - 2a^2)/(4a^4)