Answer
$(x+5)^2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
x^2+10x+25
,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$ in the quadratic expression $x^2+bx+c.$ Then, express the factored form as $(x+m_1)(x+m_2).$
$\bf{\text{Solution Details:}}$
In the given expression, the value of $c$ is $
25
$ and the value of $b$ is $
10
.$
The possible pairs of integers whose product is $c$ are
\begin{array}{l}\require{cancel}
\{ 1,25 \}, \{ 5,5 \},
\{ -1,-25 \}, \{ -5,-5 \}
.\end{array}
Among these pairs, the one that gives a sum of $b$ is $\{
5,5
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
(x+5)(x+5)
\\\\=
(x+5)^2
.\end{array}
