Question

I can show the square of a number is the same as the square of the opposite of the same number.





Hint: Make sure you have grouping symbols in the second line!!







Note:  Your calculator will have two different lines of input.

Answer 1

To show that the square of a number is the same as the square of the opposite of that number, we can use algebra.

Let \( x \) be a number.

1. The square of the number \( x \) can be written as:
\[
x^2
\]

2. The opposite of \( x \) is \( -x \), and the square of \( -x \) can be expressed as:
\[
(-x)^2
\]

3. Now, let's expand \( (-x)^2 \):
\[
(-x)^2 = (-1 \cdot x)^2 = (-1)^2 \cdot x^2 = 1 \cdot x^2 = x^2
\]

4. Thus, we have shown that:
\[
x^2 = (-x)^2
\]

By using the grouping symbols as hinted, we can emphasize the process more clearly:

- For the step \( (-x)^2 \), we can write it with grouping:
\[
(-x)^2 = (-1 \cdot (x))^2 = (-1)^2 \cdot (x)^2 = 1 \cdot x^2 = x^2
\]

So, it follows that the square of a number is indeed the same as the square of its opposite:
\[
x^2 = (-x)^2
\]

This concludes the demonstration!