1. **State the problem:** Factor the quadratic expression $x^2 + 6x + 9$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 3. **Apply to the problem:** Here, $a=1$, $b=6$, and $c=9$. We need two numbers that multiply to $1 \times 9 = 9$ and add to $6$. 4. **Find the numbers:** The numbers $3$ and $3$ satisfy this because $3 \times 3 = 9$ and $3 + 3 = 6$. 5. **Write the factored form:** Using these numbers, the factorization is $(x + 3)(x + 3)$ or $(x + 3)^2$. 6. **Verify:** Expanding $(x + 3)^2$ gives $x^2 + 6x + 9$, confirming the factorization is correct. **Final answer:** $$x^2 + 6x + 9 = (x + 3)^2$$