Q. 211 - Intermediate Algebra

Question

In the following exercises, multiply:

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

Step-by-Step Solution

Answer

By multiplying the expression we get, $-227.$

Step 1. Multiply the given expression

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

Multiply, using the Product of Conjugates Pattern

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

Step 2. Simplify

By simplifying we get,

$$\begin{gathered} =4^2-{\left(9\sqrt{3}\right)}^2 \\ =16-243 \\ =-227. \end{gathered}$$