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Multiply the expression:

[tex](13x + 7)(13x - 7)[/tex]

Choose the correct option:

A. [tex]169x^2 + 182x - 49[/tex]
B. [tex]169x^2 - 49[/tex]
C. [tex]x^2 - 49[/tex]
D. [tex]169x^2 - 182x - 49[/tex]

Answer :

To solve the problem of multiplying [tex]\((13x + 7)(13x - 7)\)[/tex], we use a special algebraic identity known as the difference of squares. This identity states that:

[tex]\((a + b)(a - b) = a^2 - b^2\)[/tex].

In our problem, let:

- [tex]\(a = 13x\)[/tex]
- [tex]\(b = 7\)[/tex]

Now, apply the identity:

1. Calculate [tex]\(a^2\)[/tex]:
- [tex]\(a = 13x\)[/tex]
- So, [tex]\(a^2 = (13x)^2 = 169x^2\)[/tex]

2. Calculate [tex]\(b^2\)[/tex]:
- [tex]\(b = 7\)[/tex]
- So, [tex]\(b^2 = 7^2 = 49\)[/tex]

3. Apply the difference of squares formula:
- [tex]\(a^2 - b^2 = 169x^2 - 49\)[/tex]

By simplifying the expression [tex]\((13x + 7)(13x - 7)\)[/tex] using the difference of squares, we obtain the result:

[tex]\[
169x^2 - 49
\][/tex]

That's your answer!

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