Question

question
factor completely.
$9x^2 - 49$

Explanation:

Step1: Identify the form

The expression \(9x^2 - 49\) is a difference of squares. The formula for factoring a difference of squares is \(a^2 - b^2=(a + b)(a - b)\). Here, \(a = 3x\) because \((3x)^2=9x^2\), and \(b = 7\) because \(7^2 = 49\).

Step2: Apply the formula

Using the difference of squares formula \(a^2 - b^2=(a + b)(a - b)\) with \(a = 3x\) and \(b = 7\), we substitute these values into the formula. So \(9x^2-49=(3x)^2 - 7^2=(3x + 7)(3x - 7)\).

Answer:

\((3x + 7)(3x - 7)\)