Can someone help me complete the perfect square with this trinomial, I don't understand how to do it. Thanks

Question

1/(x^8) -1/(x^4) +1

Answer 1

It's easier if you rewrite it as

u = 1/x^4
u^2-u+1
= u^2-u+1/4 + 3/4
= (u - 1/2)^2 + 3/4
= (1/x^4 - 1/2)^2 + 3/4