Answer
$x^2+8x+15$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the Distributive Property, the given expression, $
(x+3)(x+5)
,$ is equivalent to
\begin{array}{l}\require{cancel}
x(x)+x(5)+3(x)+3(5)
\\\\=
x^2+5x+3x+15
\\\\=
x^2+8x+15
.\end{array}