Question

factor completely.
9w² - 36

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(9w^2\) and \(36\) is \(9\). So we factor out \(9\) from the expression:
\(9w^2 - 36 = 9(w^2 - 4)\)

Step2: Apply difference of squares

Notice that \(w^2 - 4\) is a difference of squares, which can be factored as \(a^2 - b^2=(a + b)(a - b)\). Here, \(a = w\) and \(b = 2\), so:
\(w^2 - 4=(w + 2)(w - 2)\)

Step3: Combine the factors

Substitute the factored form of \(w^2 - 4\) back into the expression from Step1:
\(9(w^2 - 4)=9(w + 2)(w - 2)\)

Answer:

\(9(w + 2)(w - 2)\)