Answer
$x^4+3x^3+5x^2+7x+4$
Work Step by Step
Using the Distributive Property, the given expression, $
(x+1)(x^3+2x^2+3x+4)
,$ is equivalent to
\begin{array}{l}\require{cancel}
x(x^3)+x(2x^2)+x(3x)+x(4)+1(x^3)+1(2x^2)+1(3x)+1(4)
\\\\=
x^4+2x^3+3x^2+4x+x^3+2x^2+3x+4
\\\\=
x^4+(2x^3+x^3)+(3x^2+2x^2)+(4x+3x)+4
\\\\=
x^4+3x^3+5x^2+7x+4
.\end{array}