Chapter 4 - Section 4.4 - Multiplying Polynomials - 4.4 Exercises - Page 304: 18

$p^3-2p^2-24p$

Using the Distributive Property, the product of the given expression, $ p(p+4)(p-6) ,$ is \begin{array}{l}\require{cancel} [p(p)+p(4)](p-6) \\\\= [p^2+4p](p-6) \\\\= p^2(p)+p^2(-6)+4p(p)+4p(-6) \\\\= p^3-6p^2+4p^2-24p \\\\= p^3-2p^2-24p .\end{array}