Answer
$x^2+10x+21$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(x+7)(x+3)
$, is equivalent to
\begin{array}{l}\require{cancel}
x(x)+x(3)+7(x)+7(3)
\\\\=
x^2+3x+7x+21
\\\\=
x^2+10x+21
.\end{array}