Answer
$4a^4+16a^3+20a^2+8a+1$
Work Step by Step
Using the square of a binomial, $(a+b)^2=a^2+2(a)(b)+b^2$, the given expression is equivalent to
\begin{align*}
&
[(2a^2+4a)+1]^2
\\\\&=
(2a^2+4a)^2+2(2a^2+4a)(1)+(1)^2
\\\\&=
(2a^2+4a)^2+4a^2+8a+1
\\\\&=
(2a^2)^2+2(2a^2)(4a)+(4a)^2+4a^2+8a+1
\\\\&=
4a^4+8a(2a^2)+16a^2+4a^2+8a+1
\\\\&=
4a^4+16a^3+16a^2+4a^2+8a+1
\\\\&=
4a^4+16a^3+20a^2+8a+1
.\end{align*}
