1. **State the problem:** Simplify the expression $$(2x+1)^2$$. 2. **Recall the formula:** The square of a binomial $$(a+b)^2$$ is given by $$a^2 + 2ab + b^2$$. 3. **Identify terms:** Here, $$a = 2x$$ and $$b = 1$$. 4. **Apply the formula:** $$ (2x+1)^2 = (2x)^2 + 2 \times (2x) \times 1 + 1^2 $$ 5. **Calculate each term:** $$ (2x)^2 = 4x^2 $$ $$ 2 \times (2x) \times 1 = 4x $$ $$ 1^2 = 1 $$ 6. **Combine all terms:** $$ 4x^2 + 4x + 1 $$ **Final answer:** $$4x^2 + 4x + 1$$