#### Answer

$x^2y^2-1$

#### Work Step by Step

Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the given expression, $
(xy+1)(xy-1)
,$ is equivalent to
\begin{array}{l}\require{cancel}
(xy)^2-(1)^2
\\\\=
x^2y^2-1
.\end{array}