Question 134112
In the most general terms, {{{a^2+b^2}}} CAN be factored.  And the factors are: {{{(a+bi)(a-bi)}}} where {{{i}}} is the imaginary number defined by {{{i^2=-1}}}.  On the other hand, {{{a^2+b^2}}} cannot be factored over the real numbers because there is no real number {{{x}}} such that {{{x^2=-1}}}.