(1) a^4-b^4
=(a^2-b^2)(a^2+b^2)
=(a-b)(a+b)(a+bi)(a-bi)
(2) x^2+4
=(x+2i)(x-2i)
(3) x^2+2x+5
=(x^2+2x+1)+4
=(x+1)^2-(2i)^2
=x+1-2i)(x+1+2i)
(4) a^2+b^2+c^2+2ab
=(a^2+b^2+2ab)+c^2
=(a+b)^2-(ci)^2
=(a+b+ci)(a+b-ci)