1. The problem is to factor the expression $x^2 + 9$. 2. Recognize that the expression $x^2 + 9$ is a sum of squares, not a difference of squares. The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$, which does not apply here because of the plus sign. 3. The sum of squares $a^2 + b^2$ cannot be factored over the real numbers using real coefficients. It is considered prime in real numbers. 4. However, if we allow complex numbers, the sum of squares can be factored using the formula: $$a^2 + b^2 = (a - bi)(a + bi)$$ where $i$ is the imaginary unit with $i^2 = -1$. 5. Applying this to $x^2 + 9$, we have $a = x$ and $b = 3$, so: $$x^2 + 9 = (x - 3i)(x + 3i)$$ 6. Therefore, the expression $x^2 + 9$ cannot be factored into real linear factors but can be factored into complex linear factors as shown. Final answer: $$x^2 + 9 = (x - 3i)(x + 3i)$$