Question 891484
When you look at the difference of two squares,
{{{x^2-a^2=(x+a)(x-a)}}}
since,
{{{(x+a)(x-a)=x2-ax+ax-a^2}}} so the x terms cancel out.
However when you look at the sum of two squares,
{{{x^2+a^2}}} you have the same situation with trying to cancel out the {{{x}}} terms, however if you look at {{{(x+a)(x+a)}}} you get,
{{{(x+a)(x+a)=x^2+2ax+a^2}}}} so that won't work.
You need the opposite signs to cancel out the x terms and you need the {{{a^2}}} term to have a negative coefficient.
Since {{{i^2=-1}}} then you can use {{{i}}} as the coefficient. 
{{{(x-ai)(x+ai)=x^2+aix-aix+(ai)^2}}}
{{{(x-ai)(x+ai)=x^2-a^2}}}