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What expression is represented by the factorization below?

[tex](x+13)(x-13)[/tex]

A. [tex]x^2 - 169[/tex]

B. [tex]x^2 - 26x + 169[/tex]

C. [tex]x^2 + 169[/tex]

D. [tex]x^2 + 26x + 169[/tex]

Answer :

Sure, let’s solve it step-by-step!

We are given the expression [tex]\((x+13)(x-13)\)[/tex] and need to find which option it represents.

1. Identify the Form of the Expression:
The given expression [tex]\((x+13)(x-13)\)[/tex] is a difference of squares. The difference of squares formula is:
[tex]\[
(a+b)(a-b) = a^2 - b^2
\][/tex]

2. Apply the Formula:
Here, [tex]\(a = x\)[/tex] and [tex]\(b = 13\)[/tex]. Plugging these into the formula, we get:
[tex]\[
(x+13)(x-13) = x^2 - 13^2
\][/tex]

3. Calculate [tex]\(13^2\)[/tex]:
[tex]\[
13^2 = 169
\][/tex]

4. Simplify the Expression:
Substituting [tex]\(13^2\)[/tex] with 169, we get:
[tex]\[
x^2 - 169
\][/tex]

5. Match with the Given Options:
Now we compare the simplified expression [tex]\(x^2 - 169\)[/tex] with the provided choices:
- A. [tex]\(x^2 - 169\)[/tex]
- B. [tex]\(x^2 - 26x + 169\)[/tex]
- C. [tex]\(x^2 + 169\)[/tex]
- D. [tex]\(x^2 + 26x + 169\)[/tex]

The correct choice is:
- A. [tex]\(x^2 - 169\)[/tex]

So, the expression [tex]\((x+13)(x-13)\)[/tex] is represented by [tex]\(x^2 - 169\)[/tex].

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