1. **State the problem:** Simplify the product using the distributive property: $$(3w + 9)(7w - 8)$$ 2. **Recall the distributive property:** To multiply two binomials, multiply each term in the first binomial by each term in the second binomial. 3. **Apply the distributive property:** $$3w \times 7w = 21w^2$$ $$3w \times (-8) = -24w$$ $$9 \times 7w = 63w$$ $$9 \times (-8) = -72$$ 4. **Combine all terms:** $$21w^2 - 24w + 63w - 72$$ 5. **Simplify like terms:** $$-24w + 63w = 39w$$ 6. **Final simplified expression:** $$(3w + 9)(7w - 8) = 21w^2 + 39w - 72$$