1. **State the problem:** Simplify the expression $$(x+1)(x-1)$$. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials): $$ (a+b)(c+d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (x+1)(x-1) = x \cdot x + x \cdot (-1) + 1 \cdot x + 1 \cdot (-1) $$ 4. **Simplify each term:** $$ = x^2 - x + x - 1 $$ 5. **Combine like terms:** $$ -x + x = 0 $$ 6. **Final simplified expression:** $$ x^2 - 1 $$ This is a difference of squares, a common algebraic identity where $$(a+b)(a-b) = a^2 - b^2$$. **Answer:** $$x^2 - 1$$