Answer
$18a^4+0.8a^3+4.5a+0.2$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(9a+0.4)(2a^3+0.5)
$, is equivalent to
\begin{array}{l}\require{cancel}
9a(2a^3)+9a(0.5)+0.4(2a^3)+0.4(0.5)
\\\\=
18a^4+4.5a+0.8a^3+0.2
\\\\=
18a^4+0.8a^3+4.5a+0.2
.\end{array}
