1. **State the problem:** Simplify the expression $$(a+1)(a-2)$$. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials): $$ (x+y)(z+w) = xz + xw + yz + yw $$ 3. **Apply the formula:** $$ (a+1)(a-2) = a \cdot a + a \cdot (-2) + 1 \cdot a + 1 \cdot (-2) $$ 4. **Simplify each term:** $$ a^2 - 2a + a - 2 $$ 5. **Combine like terms:** $$ a^2 - a - 2 $$ 6. **Final answer:** $$ a^2 - a - 2 $$ This is the expanded and simplified form of the product of the two binomials.