Question

question
factor completely.
$25x^2 - 144$

Explanation:

Step1: Identify the form

The expression \(25x^2 - 144\) is a difference of squares. The formula for factoring a difference of squares is \(a^2 - b^2=(a + b)(a - b)\). Here, \(a = 5x\) because \((5x)^2=25x^2\), and \(b = 12\) because \(12^2 = 144\).

Step2: Apply the formula

Using the difference of squares formula \(a^2 - b^2=(a + b)(a - b)\) with \(a = 5x\) and \(b = 12\), we substitute these values into the formula. So \(25x^2-144=(5x)^2 - 12^2=(5x + 12)(5x - 12)\).

Answer:

\((5x + 12)(5x - 12)\)