Chapter 11.9, Problem 4WE

To determine

Simplify.

Answer to Problem 4WE

The simplified form of $\left(\sqrt{19}-9\right)\left(\sqrt{19}+9\right)$ is $-62$ .

Explanation of Solution

Given information:

The expression $\left(\sqrt{19}-9\right)\left(\sqrt{19}+9\right)$ .

Formula used:

  $\left(a+b\right)\left(a-b\right)=a^2-b^2$

  $\left(\sqrt{19}-9\right)\left(\sqrt{19}+9\right)$

As the expression resembles $\left(a+b\right)\left(a-b\right)$ ,

we will use identity $\left(a+b\right)\left(a-b\right)=a^2-b^2$

  $\begin{array}{l}\left(\sqrt{19}-9\right)\left(\sqrt{19}+9\right)\\ ={\left(\sqrt{19}\right)}^2-9^2\\ =19-81\\ =\boxed{-62}\end{array}$

The simplified form of $\left(\sqrt{19}-9\right)\left(\sqrt{19}+9\right)$ is $-62$ .