Q. 213. - Intermediate Algebra

Question

In the following exercises, multiply: 

$\left(12-5\sqrt{5}\right)\left(12+5\sqrt{5}\right)$

Step-by-Step Solution

Answer

By multiplying the expression we get, $19.$

Step 1. Multiply the given expression

The given expression is $\left(12-5\sqrt{5}\right)\left(12+5\sqrt{5}\right).$

Multiply, using the Product of Conjugates Pattern

$$\begin{gathered} \left(12-5\sqrt{5}\right)\left(12+5\sqrt{5}\right) \\ ={12}^2-{\left(5\sqrt{5}\right)}^2 \end{gathered}$$

Step 2. Simplify

By simplifying we get,

$$\begin{gathered} ={12}^2-{\left(5\sqrt{5}\right)}^2 \\ =144-125 \\ =19 \end{gathered}$$