Answer
$m^2-2n^2-3k^2+mn-2km+5kn$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
(m-n+k)(m+2n-3k)
,$ is
\begin{array}{l}\require{cancel}
m(m)+m(2n)+m(-3k)-n(m)-n(2n)-n(-3k)+k(m)+k(2n)+k(-3k)
\\\\=
m^2+2mn-3km-mn-2n^2+3kn+km+2kn-3k^2
\\\\=
m^2-2n^2-3k^2+(2mn-mn)+(-3km+km)+(3kn+2kn)
\\\\=
m^2-2n^2-3k^2+mn-2km+5kn
.\end{array}
