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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 the problem step by step.

We have the expression [tex]\((x+13)(x-13)\)[/tex].

To expand this, we can use the distributive property, commonly known as the FOIL method. FOIL stands for First, Outer, Inner, Last, which are the terms we need to multiply together.

1. First: Multiply the first terms in each binomial:
[tex]\[
x \cdot x = x^2
\][/tex]

2. Outer: Multiply the outer terms:
[tex]\[
x \cdot (-13) = -13x
\][/tex]

3. Inner: Multiply the inner terms:
[tex]\[
13 \cdot x = 13x
\][/tex]

4. Last: Multiply the last terms:
[tex]\[
13 \cdot (-13) = -169
\][/tex]

Now, we combine all these results together:
[tex]\[
x^2 - 13x + 13x - 169
\][/tex]

Next, we combine the like terms [tex]\(-13x\)[/tex] and [tex]\(13x\)[/tex]:
[tex]\[
x^2 - 13x + 13x - 169 = x^2 - 169
\][/tex]

So, the expanded expression is:
[tex]\[
(x+13)(x-13) = x^2 - 169
\][/tex]

Therefore, the correct answer is:
[tex]\[
\boxed{A. \ x^2 - 169}
\][/tex]

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