Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 26

$3-2\sqrt[3]{3}$

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $ \sqrt[3]{3}(\sqrt[3]{9}-\sqrt[3]{8}) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{3}(\sqrt[3]{9})-\sqrt[3]{3}(\sqrt[3]{8}) \\\\= \sqrt[3]{27}-\sqrt[3]{24} \\\\= \sqrt[3]{27}-\sqrt[3]{8\cdot3} \\\\= \sqrt[3]{(3)^3}-\sqrt[3]{(2)^3\cdot3} \\\\= 3-2\sqrt[3]{3} .\end{array}