Q. 210 - Intermediate Algebra

Question

In the following exercises, multiply: 

$\left(7+\sqrt{10}\right)\left(7-\sqrt{10}\right)$

Step-by-Step Solution

Answer

By multiplying the expression we get, $39.$

Step 1. Multiply the given expression

The given expression is $\left(7+\sqrt{10}\right)\left(7-\sqrt{10}\right).$

Multiply, using the Product of Conjugates Pattern

$$\begin{gathered} \left(7+\sqrt{10}\right)\left(7-\sqrt{10}\right) \\ =7^2-{\left(\sqrt{10}\right)}^2 \end{gathered}$$

Step 2. Simplify

By simplifying we get,

$$\begin{gathered} =7^2-{\left(\sqrt{10}\right)}^2 \\ =49-10 \\ =39 \end{gathered}$$