Chapter 4 - Polynomials - 4.7 Polynomials in Several Variables - 4.7 Exercise Set - Page 284: 52

$12x^2y^2+2xy-2$

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $ (3xy-1)(4xy+2) ,$ simplifies to \begin{array}{l}\require{cancel} 3xy(4xy)+3xy(2)-1(4xy)-1(2) \\\\= 12x^2y^2+6xy-4xy-2 \\\\= 12x^2y^2+2xy-2 .\end{array}