The problem asks us to factor the expression $16x^2 - 36$ by first looking for the greatest common factor (GCF).

1. Problem Description

The problem asks us to factor the expression $16x^2 - 36$ by first looking for the greatest common factor (GCF).

2. Solution Steps

First, we identify the GCF of the coefficients 16 and

3

6. The factors of 16 are 1, 2, 4, 8, and

1

6. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and

3

6. The greatest common factor of 16 and 36 is

4. Since the first term contains $x^2$ and the second term does not contain $x$, the GCF does not include any $x$ terms.

Thus, the GCF of $16x^2$ and $36$ is

4. Now we factor out the GCF from the expression:

$16x^2 - 36 = 4(4x^2 - 9)$.

The expression inside the parenthesis, $4x^2 - 9$, is a difference of squares.

We can rewrite $4x^2$ as $(2x)^2$ and 9 as $3^2$.

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

In this case, $a = 2x$ and $b = 3$.

So, $4x^2 - 9 = (2x - 3)(2x + 3)$.

Therefore, $16x^2 - 36 = 4(4x^2 - 9) = 4(2x - 3)(2x + 3)$.

3. Final Answer

The factored expression is $4(2x-3)(2x+3)$.