Answer
$(5x+4)^2$
Work Step by Step
The two numbers whose product is $
25(16)=40
$ and whose sum is $
40
$ are $\{
20,20
\}$. Using these numbers to decompose the middle term of the trinomial results to
\begin{array}{l}
25x^2+40x+16
\\=
25x^2+20x+20x+16
\\=
(25x^2+20x)+(20x+16)
\\=
5x(5x+4)+4(5x+4)
\\=
(5x+4)(5x+4)
\\=
(5x+4)^2
.\end{array}
