Chapter 11.9, Problem 16WE

To determine

Simplify.

Answer to Problem 16WE

The simplified form of $\left(8\sqrt{11}+2\sqrt{6}\right)\left(8\sqrt{11}-2\sqrt{6}\right)$ is $680$ .

Explanation of Solution

Given information:

The expression $\left(8\sqrt{11}+2\sqrt{6}\right)\left(8\sqrt{11}-2\sqrt{6}\right)$ .

Formula used:

  $\left(a+b\right)\left(a-b\right)=a^2-b^2$

  $\left(8\sqrt{11}+2\sqrt{6}\right)\left(8\sqrt{11}-2\sqrt{6}\right)$

As the expression resembles $\left(a+b\right)\left(a-b\right)$ ,

we will use identity $\left(a+b\right)\left(a-b\right)=a^2-b^2$

  $\begin{array}{l}\left(8\sqrt{11}+2\sqrt{6}\right)\left(8\sqrt{11}-2\sqrt{6}\right)\\ ={\left(8\sqrt{11}\right)}^2-{\left(2\sqrt{6}\right)}^2\\ =64\cdot 11-4\cdot 6\\ =704-24\end{array}$

  $=\boxed{680}$

The simplified form of $\left(8\sqrt{11}+2\sqrt{6}\right)\left(8\sqrt{11}-2\sqrt{6}\right)$ is $680$ .