1. **State the problem:** Simplify the expression $$(q+2)(q-3)$$. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL method): $$ (a+b)(c+d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (q+2)(q-3) = q \cdot q + q \cdot (-3) + 2 \cdot q + 2 \cdot (-3) $$ 4. **Calculate each term:** $$ q^2 - 3q + 2q - 6 $$ 5. **Combine like terms:** $$ q^2 - \cancel{3q} + \cancel{2q} - 6 = q^2 - q - 6 $$ 6. **Final answer:** $$ q^2 - q - 6 $$ This is the simplified form of the product of the two binomials.