Answer
$(5x+2)(5x+8)$
Work Step by Step
Let $z=(5x+1)$. Then the given expression, $
(5x+1)^2+8(5x+1)+7
$, is equivalent to $
z^2+8z+7
$.
The two numbers whose product is $ac=
1(7)=7
$ and whose sum is $b=
8
$ are $\{
1,7
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
z^2+8z+7
$, is
\begin{array}{l}\require{cancel}
z^2+z+7z+7
\\\\=
(z^2+z)+(7z+7)
\\\\=
z(z+1)+7(z+1)
\\\\=
(z+1)(z+7)
.\end{array}
Since $z=(5x+1)$, then,
\begin{array}{l}
(z+1)(z+7)
\\\\=
(5x+1+1)(5x+1+7)
\\\\=
(5x+2)(5x+8)
.\end{array}
