1. **State the problem:** Simplify and expand the expression $$(3\sqrt{x} - 3)^2$$. 2. **Formula used:** The square of a binomial $$(a - b)^2 = a^2 - 2ab + b^2$$. 3. **Identify terms:** Here, $a = 3\sqrt{x}$ and $b = 3$. 4. **Apply the formula:** $$ (3\sqrt{x} - 3)^2 = (3\sqrt{x})^2 - 2 \times 3\sqrt{x} \times 3 + 3^2 $$ 5. **Calculate each term:** - $$(3\sqrt{x})^2 = 9x$$ - $$-2 \times 3\sqrt{x} \times 3 = -18\sqrt{x}$$ - $$3^2 = 9$$ 6. **Combine all terms:** $$ 9x - 18\sqrt{x} + 9 $$ 7. **Final answer:** $$(3\sqrt{x} - 3)^2 = 9x - 18\sqrt{x} + 9$$