1. **State the problem:** Expand and simplify the expression $$(2t - 5)^2$$. 2. **Formula used:** The square of a binomial $$(a - b)^2 = a^2 - 2ab + b^2$$. 3. **Apply the formula:** Here, $a = 2t$ and $b = 5$. 4. **Calculate each term:** - $a^2 = (2t)^2 = 4t^2$ - $-2ab = -2 \times 2t \times 5 = -20t$ - $b^2 = 5^2 = 25$ 5. **Combine all terms:** $$4t^2 - 20t + 25$$ 6. **Final answer:** The expanded form of $$(2t - 5)^2$$ is $$4t^2 - 20t + 25$$.