Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 30

$9\sqrt[]{10}-6\sqrt[]{14}$

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $ 3\sqrt[]{2}(3\sqrt[]{5}-2\sqrt[]{7}) ,$ simplifies to \begin{array}{l}\require{cancel} 3\sqrt[]{2}(3\sqrt[]{5})-3\sqrt[]{2}(2\sqrt[]{7}) \\\\= 9\sqrt[]{10}-6\sqrt[]{14} .\end{array}