Which of the following represents the factorization of \(x^2 - 9\)?

To factor the expression (x^2 - 9), one can recognize that it is a difference of squares. The difference of squares formula is expressed as (a^2 - b^2 = (a - b)(a + b)). In this case, (x^2) can be identified as (a^2) (where (a = x)) and (9) as (b^2) (where (b = 3)).

Applying the formula, we substitute (a) and (b) accordingly:

[

x^2 - 9 = x^2 - 3^2

]

This leads to the factorization:

[

(x - 3)(x + 3)

]

So, the correct representation of the factorization of (x^2 - 9) is ((x - 3)(x + 3)).

This result aligns perfectly with the properties of quadratic expressions and shows a clear understanding of how to apply the difference of squares theorem. The other options do not follow this principle or misapply the process of factoring. Thus, option A successfully represents the factorization of the expression (x^2 -