Question

factor completely.
$16g^2 - 1$

Explanation:

Step1: Recognize the difference of squares

The expression \(16g^2 - 1\) can be written as \((4g)^2 - 1^2\), which is a difference of squares. The formula for factoring a difference of squares is \(a^2 - b^2=(a + b)(a - b)\).

Step2: Apply the difference of squares formula

Here, \(a = 4g\) and \(b = 1\). Substituting these into the formula, we get \((4g + 1)(4g - 1)\).

Answer:

\((4g + 1)(4g - 1)\)