1. **State the problem:** We need to expand and simplify the expression $$(3 - ext{lne})^3$$. 2. **Recall the formula:** The cube of a binomial $(a - b)^3$ is expanded as: $$a^3 - 3a^2b + 3ab^2 - b^3$$ 3. **Identify terms:** Here, $a = 3$ and $b = \text{lne}$. 4. **Calculate each term:** - $a^3 = 3^3 = 27$ - $3a^2b = 3 \times 3^2 \times \text{lne} = 3 \times 9 \times \text{lne} = 27\text{lne}$ - $3ab^2 = 3 \times 3 \times (\text{lne})^2 = 9(\text{lne})^2$ - $b^3 = (\text{lne})^3$ 5. **Put it all together:** $$ (3 - \text{lne})^3 = 27 - 27\text{lne} + 9(\text{lne})^2 - (\text{lne})^3 $$ 6. **Final answer:** $$\boxed{27 - 27\text{lne} + 9(\text{lne})^2 - (\text{lne})^3}$$