Q. 209 - Intermediate Algebra

Question

In the following exercises, multiply: 

$\left(4+\sqrt{2}\right)\left(4-\sqrt{2}\right)$

Step-by-Step Solution

Answer

By multiplying the expression we get, $14.$

Step 1. Multiply the given expression

The given expression is $(4+\sqrt{2})(4-\sqrt{2}).$

Multiply, using the Product of Conjugates Pattern

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

Step 2. Simplify

By simplifying we get,

$$\begin{gathered} 4^2-{\left(\sqrt{2}\right)}^2 \\ =16-2 \\ =14 \end{gathered}$$