Answer
$-32+36i$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method and using $i^2=-1$, the given expression $
4i(2+5i)(2-i)
,$ simplifies to
\begin{array}{l}\require{cancel}
4i[2(2)+2(-i)+5i(2)+5i(-i)]
\\\\=
4i[4-2i+10i-5i^2]
\\\\=
4i[4-2i+10i-5(-1)]
\\\\=
4i[4-2i+10i+5]
\\\\=
4i[(4+5)+(-2i+10i)]
\\\\=
4i[9+8i]
\\\\=
36i+32i^2
\\\\=
36i+32(-1)
\\\\=
36i-32
\\\\=
-32+36i
.\end{array}
