Problem 18 - Algebra 1: Concepts and Skills

Question

Factor the expression. $$ n^{2}-16 $$

Step-by-Step Solution

Answer

\(n^{2} - 16\) factors to \((n - 4)(n + 4)\)

Step 1: Identify the Coefficients

Start by identifying the coefficients a and b. In the formula \(a^2 - b^2\), \(a\) is the square root of the first term, \(n^2\), which is \(n\), and \(b\) is the square root of the second term, \(16\), which is \(4\).

Step 2: Apply the Formula

Apply the difference of squares formula, which is \((a - b)(a + b)\). Substitute \(n\) for \(a\) and \(4\) for \(b\) to get \( (n - 4)(n + 4)\)

Step 3: Check the Solution

Check the solution by expanding \((n - 4)(n + 4)\). Multiply \(n - 4\) by \(n + 4\) to get \( n^2 - 16\), which confirms that the solution is correct.