1. **State the problem:** Expand and simplify the expression $$(y + 1)(y - 2)(y + 3)$$. 2. **Recall the formula:** To expand the product of three binomials, first multiply two of them, then multiply the result by the third. 3. **Step 1: Multiply the first two binomials:** $$(y + 1)(y - 2) = y \cdot y + y \cdot (-2) + 1 \cdot y + 1 \cdot (-2) = y^2 - 2y + y - 2 = y^2 - y - 2$$ 4. **Step 2: Multiply the result by the third binomial:** $$(y^2 - y - 2)(y + 3) = y^2(y + 3) - y(y + 3) - 2(y + 3)$$ 5. **Distribute each term:** $$= y^3 + 3y^2 - y^2 - 3y - 2y - 6$$ 6. **Combine like terms:** $$= y^3 + (3y^2 - y^2) + (-3y - 2y) - 6 = y^3 + 2y^2 - 5y - 6$$ 7. **Final answer:** $$\boxed{y^3 + 2y^2 - 5y - 6}$$ This is the expanded and simplified form of the original expression.