Answer
$15x^{2}y^{2}+xy-2
$
Work Step by Step
Using $(a+b)(c+d)=ab+ad+bc+bd$ or the FOIL Method, the product of the given expression, $
(3xy-1)(5xy+2)
,$ is
\begin{array}{l}\require{cancel}
3xy(5xy)+3xy(2)-1(5xy)-1(2)
\\\\=
15x^{1+1}y^{1+1}+6xy-5xy-2
\\\\=
15x^{2}y^{2}+6xy-5xy-2
\\\\=
15x^{2}y^{2}+xy-2
.\end{array}