Q. 204 - Intermediate Algebra

Question

In the following exercises, multiply:  

$\left(4\sqrt{6}+7\sqrt{13}\right)\left(8\sqrt{6}-3\sqrt{13}\right)$

Step-by-Step Solution

Answer

On multiplication we get, $-81+44\sqrt{78}.$

Step 1. Multiply the given expression

The given expression is $\left(4\sqrt{6}+7\sqrt{13}\right)\left(8\sqrt{6}-3\sqrt{13}\right)$

By multiplying we get, 

$$\begin{gathered} \left(4\sqrt{6}+7\sqrt{13}\right)\left(8\sqrt{6}-3\sqrt{13}\right) \\ =32·6-12\sqrt{78}+56\sqrt{78}-21·13 \end{gathered}$$

Step 2. Simplify

By simplifying we get,

$$\begin{gathered} =32·6-12\sqrt{78}+56\sqrt{78}-21·13 \\ =(192-273)+\sqrt{78}(-12+56) \\ =-81+44\sqrt{78} \end{gathered}$$