Chapter 4 - Section 4.4 - Multiplying Polynomials - 4.4 Exercises - Page 304: 43

$12c^{2}+16cd-3d^{2}$

We are given the expression $(6c-d)(2c+3d)$. We can find the product of this expression using the FOIL method. First terms: $6c\times 2c=12c^{2}$ Outer terms: $6c\times3d=18cd$ Inner terms: $-d\times 2c=-2cd$ Last terms: $-d\times3d=-3d^{2}$ Adding together: $12c^{2}+18cd+(-2cd)+(-3d^{2})=12c^{2}+18cdk-2cd-3d^{2}=12c^{2}+16cd-3d^{2}$