Answer
$x^3+3x^2+5x+3$
Work Step by Step
Using the Distributive Property, the given expression, $
(x+1)(x^2+2x+3)
,$ is equivalent to
\begin{array}{l}\require{cancel}
x(x^2)+x(2x)+x(3)+1(x^2)+1(2x)+1(3)
\\\\=
x^3+2x^2+3x+x^2+2x+3
\\\\=
x^3+(2x^2+x^2)+(3x+2x)+3
\\\\=
x^3+3x^2+5x+3
.\end{array}