Answer
$x^4+5x^3+11x^2+10x+3$
Work Step by Step
Using the Distributive Property, the given expression, $
(x+1)(x^3+4x^2+7x+3)
,$ is equivalent to
\begin{array}{l}\require{cancel}
x(x^3)+x(4x^2)+x(7x)+x(3)+1(x^3)+1(4x^2)+1(7x)+1(3)
\\\\=
x^4+4x^3+7x^2+3x+x^3+4x^2+7x+3
\\\\=
x^4+(4x^3+x^3)+(7x^2+4x^2)+(3x+7x)+3
\\\\=
x^4+5x^3+11x^2+10x+3
.\end{array}
