Chapter 6 - Radical Functions and Rational Exponents - 6-3 Binomial Radical Expressions - Practice and Problem-Solving Exercises - Page 378: 31

$-40$

Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the given expression, $ (2\sqrt{6}+8)(2\sqrt{6}-8) ,$ is equivalent to \begin{align*} & (2\sqrt{6})^2-(8)^2 \\&= 4(6)-64 \\&= 24-64 \\&= -40 .\end{align*}