1. **State the problem:** Simplify the expression $$(a-b)(2a+b)$$. 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:** $$(a-b)(2a+b) = a(2a+b) - b(2a+b)$$ 4. **Multiply each term:** $$a \cdot 2a = 2a^2$$ $$a \cdot b = ab$$ $$-b \cdot 2a = -2ab$$ $$-b \cdot b = -b^2$$ 5. **Combine all terms:** $$2a^2 + ab - 2ab - b^2$$ 6. **Simplify like terms:** $$ab - 2ab = -ab$$ 7. **Final simplified expression:** $$2a^2 - ab - b^2$$