Q. 212 - Intermediate Algebra

Question

In the following exercises, multiply: 

$\left(1+8\sqrt{2}\right)\left(1-8\sqrt{2}\right)$

Step-by-Step Solution

Answer

By multiplying the expression we get, $-127.$

Step 1. Multiply the given expression

The given expression is $\left(1+8\sqrt{2}\right)\left(1-8\sqrt{2}\right).$

Multiply, using the Product of Conjugates Pattern

$$\begin{gathered} \left(1+8\sqrt{2}\right)\left(1-8\sqrt{2}\right) \\ =1^2-{\left(8\sqrt{2}\right)}^2 \end{gathered}$$

Step 2. Simplify

By simplifying we get,

$$\begin{gathered} =1^2-{\left(8\sqrt{2}\right)}^2 \\ =1-128 \\ =-127 \end{gathered}$$