Answer
$3t^3-19t^2+23t-4$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
(3t-4)(t^2-5t+1)
,$ is
\begin{array}{l}\require{cancel}
3t(t^2)+3t(-5t)+3t(1)-4(t^2)-4(-5t)-4(1)
\\\\=
3t^3-15t^2+3t-4t^2+20t-4
\\\\=
3t^3+(-15t^2-4t^2)+(3t+20t)-4
\\\\=
3t^3-19t^2+23t-4
.\end{array}