Q. 203 - Intermediate Algebra

Question

In the following exercises, multiply: 

$\left(2\sqrt{7}-5\sqrt{11}\right)\left(4\sqrt{7}+9\sqrt{11}\right)$

Step-by-Step Solution

Answer

On multiplication we get, $-439-2\sqrt{77}.$

Step 1. Multiply the given expression

The given expression is $\left(2\sqrt{7}-5\sqrt{11}\right)\left(4\sqrt{7}+9\sqrt{11}\right)$

By multiplying we get,

$$\begin{gathered} \left(2\sqrt{7}-5\sqrt{11}\right)\left(4\sqrt{7}+9\sqrt{11}\right) \\ =8·7+18\sqrt{77}-20\sqrt{77}-45·11 \end{gathered}$$

Step 2. Simplify

By simplifying we get, 

$$\begin{gathered} =8·7+18\sqrt{77}-20\sqrt{77}-45·11 \\ =(56-495)+\sqrt{77}(18-20) \left[combine the like term\right] \\ =-439-2\sqrt{77} \end{gathered}$$