Problem 2 - Algebra 1: Concepts and Skills

Question

Factor the expression. $$ x^{2}-9 $$

Step-by-Step Solution

Answer

The factored form of the expression is \((x - 3)(x + 3)\)

Step 1: Identify the Form

The given expression is \(x^{2}-9\). Notice the expression is in the form \(a^2 - b^2\), which is known as difference of squares where \(a = x\) and \(b = 3\)

Step 2: Apply the Difference of Squares Formula

The formula for factoring difference of squares is \(a^2 - b^2 = (a - b)(a + b)\). Substituting \(a = x\) and \(b = 3\) into the formula, the factored form becomes \((x - 3)(x + 3)\)

Step 3: Final Answer

The factored form of the expression \(x^{2}-9\) is \((x - 3)(x + 3)\)