1. **State the problem:** Simplify the expression $(x+9)(x-8)$. 2. **Use the distributive property (FOIL method) for binomials:** $$ (x+9)(x-8) = x \cdot x + x \cdot (-8) + 9 \cdot x + 9 \cdot (-8) $$ 3. **Calculate each term:** $$ x^2 - 8x + 9x - 72 $$ 4. **Combine like terms:** $$ x^2 + ( -8x + 9x ) - 72 = x^2 + x - 72 $$ 5. **Final simplified expression:** $$ x^2 + x - 72 $$ This is the expanded and simplified form of the product of the two binomials.