1. **State the problem:** Simplify the expression $$(p+q)(p-q)+3(p+2q)$$. 2. **Use the distributive property and difference of squares formula:** $$(p+q)(p-q) = p^2 - q^2$$ This is because $$(a+b)(a-b) = a^2 - b^2$$. 3. **Expand the second term:** $$3(p+2q) = 3p + 6q$$ 4. **Rewrite the expression with these expansions:** $$p^2 - q^2 + 3p + 6q$$ 5. **Final simplified expression:** $$p^2 - q^2 + 3p + 6q$$ This is the simplified form; no like terms can be combined further.