Answer
$8x^2+30x+7$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(4x+1)(2x+7)
$, is equivalent to
\begin{array}{l}\require{cancel}
4x(2x)+4x(7)+1(2x)+1(7)
\\\\=
8x^2+28x+2x+7
\\\\=
8x^2+30x+7
.\end{array}