Chapter 9.3, Problem 44HP

To determine

Whether the statement “for any integer $a$ , ${\left(-a\right)}^2=-a^2$ ” is true or false.

Answer to Problem 44HP

The statement “for any integer $a$ , ${\left(-a\right)}^2=-a^2$ ” isfalse.

Explanation of Solution

Given information:

The statement “for any integer $a$ , ${\left(-a\right)}^2=-a^2$ ”.

Consider the provided statement “for any integer $a$ , ${\left(-a\right)}^2=-a^2$ . ”

The statement is false because ${\left(-a\right)}^2=a^2$ .

Mathematically, we can provide the counter example that let $a=2$ then ${\left(-2\right)}^2=\left(-2\right)\left(-2\right)=2^2=4$

Thus, the statement “for any integer $a$ , ${\left(-a\right)}^2=-a^2$ ” is false.