1. The problem is to factor the expression $x^2 - 49$. 2. Recognize that this is a difference of squares, which follows the formula $a^2 - b^2 = (a - b)(a + b)$. 3. Here, $x^2$ is $a^2$ and $49$ is $7^2$, so $a = x$ and $b = 7$. 4. Applying the formula, we get $x^2 - 49 = (x - 7)(x + 7)$. 5. This means the expression factors into two binomials, one subtracting 7 and one adding 7 to $x$. 6. The factored form is the simplest form and useful for solving equations or simplifying expressions involving $x^2 - 49$.