Question

15 ( 75x^2 - 9 )

Explanation:

Step1: Factor out common term

Identify and factor the GCD of 75 and 9.
$75x^2 - 9 = 3(25x^2 - 3)$

Step2: Recognize difference of squares

Rewrite $25x^2$ as $(5x)^2$ to apply the difference of squares formula $a^2 - b^2=(a-b)(a+b)$, where $a=5x$ and $b=\sqrt{3}$.
$25x^2 - 3 = (5x)^2 - (\sqrt{3})^2 = (5x - \sqrt{3})(5x + \sqrt{3})$

Step3: Combine factored terms

Substitute the factored binomial back into the expression.
$3(25x^2 - 3) = 3(5x - \sqrt{3})(5x + \sqrt{3})$

Answer:

$3(5x - \sqrt{3})(5x + \sqrt{3})$