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

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

• A. (x - 3)(x + 3)
• B. (x + 9)(x - 9)
• C. (x - 3)(x - 3)
• D. (x + 3)(x + 3)

Answer: (A)

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 -

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 -