Answer
$2a^3-9a^2+19a-15$
Work Step by Step
Using the Distributive Property, the given expression, $
(2a-3)(a^2-3a+5)
,$ is equivalent to
\begin{array}{l}\require{cancel}
2a(a^2)+2a(-3a)+2a(5)-3(a^2)-3(-3a)-3(5)
\\\\=
2a^3-6a^2+10a-3a^2+9a-15
\\\\=
2a^3+(-6a^2-3a^2)+(10a+9a)-15
\\\\=
2a^3-9a^2+19a-15
.\end{array}