Question

factor completely.
$75x^2 - 3$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of \(75x^2\) and \(3\). The GCF of 75 and 3 is 3. So we factor out 3:
\(75x^2 - 3 = 3(25x^2 - 1)\)

Step2: Apply difference of squares

Notice that \(25x^2 - 1\) is a difference of squares, since \(25x^2=(5x)^2\) and \(1 = 1^2\). The formula for difference of squares is \(a^2 - b^2=(a + b)(a - b)\). Here, \(a = 5x\) and \(b = 1\), so:
\(25x^2 - 1=(5x + 1)(5x - 1)\)

Step3: Combine the factors

Putting it all together, the completely factored form is:
\(3(5x + 1)(5x - 1)\)

Answer:

\(3(5x + 1)(5x - 1)\)