Answer
$t^2+4t-21$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(t+7)(t-3)
$, is equivalent to
\begin{array}{l}\require{cancel}
t(t)+t(-3)+7(t)+7(-3)
\\\\=
t^2-3t+7t-21
\\\\=
t^2+4t-21
.\end{array}