Chapter 12, Problem 9CLR

To determine

To Evaluate: The simplified value of the expression $\left(6-13\right)\left(6+13\right)$ .

Answer to Problem 9CLR

The value of the expression $\left(6-13\right)\left(6+13\right)$ is $-133$ .

Explanation of Solution

Given information:

The expression is $\left(6-13\right)\left(6+13\right)$ .

Formula used:

When sum of two numbers multiply with difference of those numbers will be difference of

their squares. That is

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

Calculation:

Consider the expression is $\left(6-13\right)\left(6+13\right)$ .

Recall that when sum of two numbers multiply with difference of those numbers will be

difference of their squares. That is,

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

Apply it,

  $\left(6-13\right)\left(6+13\right)=6^2-{13}^2$

Further simplify it,

  $\begin{array}{c}{6}^2-{13}^2=36-169\\ =-133\end{array}$

Thus, the value of the expression $\left(6-13\right)\left(6+13\right)$ is $-133$ .