Chapter 4 - Polynomials - 4.7 Polynomials in Several Variables - 4.7 Exercise Set - Page 284: 45

$12c^2+5cd-2d^2$

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $ (4c-d)(3c+2d) ,$ simplifies to \begin{array}{l}\require{cancel} 4c(3c)+4c(2d)-d(3c)-d(2d) \\\\= 12c^2+8cd-3cd-2d^2 \\\\= 12c^2+5cd-2d^2 .\end{array}