Answer
$m^3-7m^2p+13mp^2-15p^3$
Work Step by Step
Using the Distributive Property, the given expression, $
(m-5p)(m^2-2mp+3p^2)
,$ is equivalent to
\begin{array}{l}\require{cancel}
m(m^2)+m(-2mp)+m(3p^2)-5p(m^2)-5p(-2mp)-5p(3p^2)
\\\\=
m^3-2m^2p+3mp^2-5m^2p+10mp^2-15p^3
\\\\=
m^3+(-2m^2p-5m^2p)+(3mp^2+10mp^2)-15p^3
\\\\=
m^3-7m^2p+13mp^2-15p^3
.\end{array}