Q. 214 - Intermediate Algebra

Question

In the following exercises, multiply: 

$\left(9-4\sqrt{3}\right)\left(9+4\sqrt{3}\right)$

Step-by-Step Solution

Answer

By multiplying the expression we get, $33.$

Step 1. Multiply the given expression

The given expression is $(9-4\sqrt{3})(9+4\sqrt{3}).$

Multiply, using the Product of Conjugates Pattern

$$\begin{gathered} (9-4\sqrt{3})(9+4\sqrt{3}) \\ =9^2-{\left(4\sqrt{3}\right)}^2 \end{gathered}$$

Step 2. Simplify

By simplifying we get,

$$\begin{gathered} =9^2-{\left(4\sqrt{3}\right)}^2 \\ =81-48 \\ =33 \end{gathered}$$