Answer
$16a^4-5.6a^3-a+0.35$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(2a-0.7)(8a^3-0.5)
$, is equivalent to
\begin{array}{l}\require{cancel}
2a(8a^3)+2a(-0.5)-0.7(8a^3)-0.7(-0.5)
\\\\=
16a^4-a-5.6a^3+0.35
\\\\=
16a^4-5.6a^3-a+0.35
.\end{array}