#### Answer

$(5x+1)^2$

#### Work Step by Step

The two numbers whose product is $ac=
25(1)=25
$ and whose sum is $b=
10
$ are $\{
5,5
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
25x^2+10x+1
$, is
\begin{array}{l}\require{cancel}
25x^2+5x+5x+1
\\\\=
(25x^2+5x)+(5x+1)
\\\\=
5x(5x+1)+(5x+1)
\\\\=
(5x+1)(5x+1)
\\\\=
(5x+1)^2
.\end{array}