Answer
$18-11u^2v^2+u^4v^4$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(9-u^2v^2)(2-u^2v^2)
,$ simplifies to
\begin{array}{l}\require{cancel}
9(2)+9(-u^2v^2)-u^2v^2(2)-u^2v^2(-u^2v^2)
\\\\=
18-9u^2v^2-2u^2v^2+u^4v^4
\\\\=
18-11u^2v^2+u^4v^4
.\end{array}