Answer
$4a^4+12a^2+9$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the Square of a Binomial, the expression, $
[(2a^2+4)-1]^2
$, is equivalent to
\begin{array}{l}
(2a^2+4)^2+2(2a^2+4)(-1)+(-1)^2
\\\\=
(2a^2)^2+2(2a^2)(4)+(4)^2+2(2a^2+4)(-1)+(-1)^2
\\\\=
4a^4+16a^2+16-4a^2-8+1
\\\\=
4a^4+(16a^2-4a^2)+(16-8+1)
\\\\=
4a^4+12a^2+9
.\end{array}
