Chapter 4 - Polynomials - 4.7 Polynomials in Several Variables - 4.7 Exercise Set - Page 284: 51

$20r^2t^2-23rt+6$

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $ (5rt-2)(4rt-3) ,$ simplifies to \begin{array}{l}\require{cancel} 5rt(4rt)+5rt(-3)-2(4rt)-2(-3) \\\\= 20r^2t^2-15rt-8rt+6 \\\\= 20r^2t^2-23rt+6 .\end{array}