Answer :

Answer:

A

Step-by-step explanation:

note that these are the factors of a difference of squares

• a² - b² = (a + b)(a - b), hence

(x + 13)(x - 13)= x² - 13² = x² - 169 → A



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Rewritten by : Barada

The expression represented by the factorization (x+13)(x-13) is [tex]x^2-169.[/tex], which corresponds to answer choice A. This is derived by multiplying the terms and combining like terms, which in this case cancel each other out.

The expression represented by the factorization (x+13)(x-13) is known as the difference of squares. When we expand this, we apply the distributive property (also known as the FOIL method). We multiply the first terms, the outer terms, the inner terms, and then the last terms together and combine like terms.

Let's multiply it out:

  1. Multiply the first terms: x x x = [tex]x^2.[/tex]
  2. Multiply the outer terms: x x -13 = -13x.
  3. Multiply the inner terms: 13 x x = +13x.
  4. Multiply the last terms: 13 x -13 = -169.

Combine like terms: the +13x and -13x cancel each other out, leaving us with:

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

Therefore, the correct expression is A. [tex]x^2-169.[/tex]