Chapter 4 - Section 4.4 - Multiplying Polynomials - 4.4 Exercises - Page 304: 19

$24z^3-20z^2-16z$

Using the Distributive Property, the product of the given expression, $ 4z(2z+1)(3z-4) ,$ is \begin{array}{l}\require{cancel} [4z(2z)+4z(1)](3z-4) \\\\= [8z^2+4z](3z-4) \\\\= 8z^2(3z)+8z^2(-4)+4z(3z)+4z(-4) \\\\= 24z^3-32z^2+12z^2-16z \\\\= 24z^3-20z^2-16z .\end{array}