Question

Why is there no sum-of-two-squares factoring pattern?

Answer 1

\[x^2+a^2=(x+ia)(x-ia)\qquad\qquad(\text{where } i^2=-1)\]

Answer 2

smartypants

Answer 3

it won't be possible if you want the factors to be real
for unreal/imaginary factors you can do what unkle did

Answer 4

\[x^2+a^2=(x+a)^2-2ax\]