Question

which equation is true?
9x² - 25 = (3x - 5)(3x - 5)
9x² - 25 = (3x - 5)(3x + 5)
9x² - 25 = -(3x + 5)(3x + 5)
9x² - 25 = -(3x + 5)(3x - 5)

Explanation:

Step1: Recall Difference of Squares

The difference of squares formula is \(a^2 - b^2=(a - b)(a + b)\).

Step2: Identify \(a\) and \(b\)

For \(9x^2-25\), we can rewrite it as \((3x)^2 - 5^2\). Here, \(a = 3x\) and \(b = 5\).

Step3: Apply the Formula

Using the difference of squares formula \(a^2 - b^2=(a - b)(a + b)\), we substitute \(a = 3x\) and \(b = 5\) to get \((3x - 5)(3x + 5)\). So \(9x^2-25=(3x - 5)(3x + 5)\).

Answer:

\(9x^2 - 25=(3x - 5)(3x + 5)\) (the second option)