1. **Problem:** Solve the equation $$y^2 - 1 = 0$$. 2. **Formula and rules:** This is a quadratic equation in terms of $y$. We can use the difference of squares factorization: $$y^2 - 1 = (y - 1)(y + 1) = 0$$ 3. **Intermediate work:** Set each factor equal to zero: $$y - 1 = 0 \implies y = 1$$ $$y + 1 = 0 \implies y = -1$$ 4. **Explanation:** The equation $y^2 - 1 = 0$ means we are looking for values of $y$ whose square is 1. Since both $1^2$ and $(-1)^2$ equal 1, these are the solutions. 5. **Final answer:** $$y = 1 \text{ or } y = -1$$