Answer
$(5x+4)^2$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
25x^2+40x+16
\end{array} has $ac=
25(16)=400
$ and $b=
40
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
20,20
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
25x^2+20x+20x+16
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(25x^2+20x)+(20x+16)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
5x(5x+4)+4(5x+4)
.\end{array}
Factoring the $GCF=
(5x+4)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(5x+4)(5x+4)
\\\\=
(5x+4)^2
.\end{array}