#### Answer

$(x+7)^2$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
x^2+14x+49
,$ 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 expression above, the value of $c$ is $
49
$ and the value of $b$ is $
14
.$
The possible pairs of integers whose product is $c$ are
\begin{array}{l}\require{cancel}
\{ 1,49 \}, \{ 7,7 \},
\\
\{ -1,-49 \}, \{ -7,-7 \}
.\end{array}
Among these pairs, the one that gives a sum of $b$ is $\{
7,7
\}.$ Hence, the factored form of the expression above is
\begin{array}{l}\require{cancel}
(x+7)(x+7)
\\\\=
(x+7)^2
.\end{array}