1. **State the problem:** Simplify the expression $$(a+b+c)(a+b-c)$$. 2. **Recall the formula:** This is a product of two binomials with a similar structure. We can use the distributive property (FOIL) to expand: $$ (x+y)(x-y) = x^2 - y^2 $$ Here, consider $x = a+b$ and $y = c$. 3. **Apply the formula:** $$ (a+b+c)(a+b-c) = (a+b)^2 - c^2 $$ 4. **Expand $(a+b)^2$:** $$ (a+b)^2 = a^2 + 2ab + b^2 $$ 5. **Substitute back:** $$ (a+b+c)(a+b-c) = a^2 + 2ab + b^2 - c^2 $$ 6. **Final simplified expression:** $$ \boxed{a^2 + 2ab + b^2 - c^2} $$ This is the simplified form of the given expression.