1. **State the problem:** Simplify the expression $$2(a+2) + (2a+1)(a-1)$$. 2. **Use distributive property:** $$2(a+2) = 2a + 4$$ 3. **Expand the second term using FOIL:** $$(2a+1)(a-1) = 2a \cdot a + 2a \cdot (-1) + 1 \cdot a + 1 \cdot (-1) = 2a^2 - 2a + a - 1$$ 4. **Combine like terms inside the second term:** $$2a^2 - 2a + a - 1 = 2a^2 - a - 1$$ 5. **Rewrite the entire expression:** $$2a + 4 + 2a^2 - a - 1$$ 6. **Combine like terms:** $$2a^2 + (2a - a) + (4 - 1) = 2a^2 + a + 3$$ 7. **Final simplified expression:** $$\boxed{2a^2 + a + 3}$$