1. **State the problem:** Simplify the expression $$(2a + x)^2 - 9$$. 2. **Recall the formula:** The square of a binomial is given by $$(A + B)^2 = A^2 + 2AB + B^2$$. 3. **Apply the formula:** Here, $A = 2a$ and $B = x$, so $$ (2a + x)^2 = (2a)^2 + 2 \cdot (2a) \cdot x + x^2 = 4a^2 + 4ax + x^2 $$. 4. **Rewrite the expression:** Substitute back into the original expression: $$ 4a^2 + 4ax + x^2 - 9 $$. 5. **Recognize the difference of squares:** The expression can be seen as $$ (2a + x)^2 - 3^2 $$, which factors as $$ (2a + x - 3)(2a + x + 3) $$. 6. **Final answer:** The simplified and factored form is $$ (2a + x - 3)(2a + x + 3) $$. This shows how to expand and factor expressions involving squares and differences of squares.