Answer
$7x^2+38xy+15y^2$
Work Step by Step
Using $(a+b)(c+d)=ab+ad+bc+bd$ or the FOIL Method, the product of the given expression, $
(x+5y)(7x+3y)
,$ is
\begin{array}{l}\require{cancel}
x(7x)+x(3y)+5y(7x)+5y(3y)
\\\\=
7x^2+3xy+35xy+15y^2
\\\\=
7x^2+38xy+15y^2
.\end{array}