Answer
$25+15x+2x^2$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(5+x)(5+2x)
$, is equivalent to
\begin{array}{l}\require{cancel}
5(5)+5(2x)+x(5)+x(2x)
\\\\=
25+10x+5x+2x^2
\\\\=
25+15x+2x^2
.\end{array}