Factor Quadratic Eba233

1. **State the problem:** We need to factor the quadratic expression $$x^2 + 6x + 9$$. 2. **Recall the factoring formula:** A quadratic expression of the form $$ax^2 + bx + c$$ can be factored as $$(x + m)(x + n)$$ where $$m$$ and $$n$$ satisfy $$m + n = b$$ and $$mn = c$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = 6$$, and $$c = 9$$. 4. **Find two numbers that add to 6 and multiply to 9:** The numbers $$3$$ and $$3$$ satisfy this because $$3 + 3 = 6$$ and $$3 \times 3 = 9$$. 5. **Write the factored form:** Therefore, $$x^2 + 6x + 9 = (x + 3)(x + 3) = (x + 3)^2$$. 6. **Final answer:** The factored form is $$\boxed{(x + 3)^2}$$.