Question

Factor the expression over the set of complex numbers.16a^4 + 4b^2

Answer 1

In order to factor this expression over the set of complex numbers, let's rewrite the second term as follows:

$4b^2=-4b^2i^2$

Then, we can use the following notable product:

$m^2-n^2=(m+n)(m-n)$

So we have:

$\begin{gathered} 16a^4-4b^2i^2\\ \\ =(4a^2)^2-(2bi)^2\\ \\ =(4a^2+2bi)(4a^2-2bi) \end{gathered}$