The problem asks us to factor the expression $9x - 36x^3$ completely, using the difference of squares formula. We are told to factor out any common factors first.

1. Problem Description

The problem asks us to factor the expression $9x - 36x^3$ completely, using the difference of squares formula. We are told to factor out any common factors first.

2. Solution Steps

First, we factor out the greatest common factor from the expression $9x - 36x^3$.

The greatest common factor of $9x$ and $36x^3$ is $9x$.

Factoring out $9x$, we get

$9x - 36x^3 = 9x(1 - 4x^2)$.

Now, we have the expression $1 - 4x^2$ which can be written as $1^2 - (2x)^2$. This is a difference of squares.

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

Applying the difference of squares formula to $1 - 4x^2$, where $a = 1$ and $b = 2x$, we get

$1 - 4x^2 = (1 - 2x)(1 + 2x)$.

Thus, $9x - 36x^3 = 9x(1 - 4x^2) = 9x(1 - 2x)(1 + 2x)$.

3. Final Answer

$9x(1 - 2x)(1 + 2x)$