Question

Factor the expression. Tell which special product factoring pattern you used. $$4 n^{2}-36$$

Short answer

The factored form of the expression \(4n^{2} - 36\) is \((2n + 6)(2n - 6)\). The special product factoring pattern used is the difference of squares.

Step-by-step solution

- Identify the Pattern

The given expression can be written in the form \(a^{2} - b^{2}\), where \(a = 2n\) and \(b = 6\). This is a difference of squares, which is a special factoring pattern.

- Apply the Difference of Squares Formula

The difference of squares formula is \((a^2 - b^2) = (a+b)(a-b)\). Substituting the values of \(a\) and \(b\) from Step 1 into the difference of squares formula, we have \((2n + 6)(2n - 6)\).

- Simplify if Necessary

Here, there is no need for further simplification as \((2n + 6)(2n - 6)\) is already in its simplest form.