Factor (x^4 + 1) as a difference of squares by first adding and subtracting the same quantity.?

Answer 1

(x^4+1)
=(x^2+i)(x^2-i)

Sarkartap done a good job
but answer wrong!
Correction:
x^4+1
=(x^2)^2+(1)^2+2x^2-2x^2
=(x^2+1)^2-(x sqrt2)^2
=(x^2+1+xsqrt2)(x^2+1-xsqrt2)

Answer 2

x^4+1
=(x^2)^2+(1)^2+2x^2-2x^2
=(x+1)^2-(x sqrt2)^2
=(x+1+xsqrt2)(x+1-xsqrt2)