Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 29

$4\sqrt[]{6}-8\sqrt[]{15}$

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $ 4\sqrt[]{3}(\sqrt[]{2}-2\sqrt[]{5}) ,$ simplifies to \begin{array}{l}\require{cancel} 4\sqrt[]{3}(\sqrt[]{2})-4\sqrt[]{3}(2\sqrt[]{5}) \\\\= 4\sqrt[]{6}-8\sqrt[]{15} .\end{array}