1. **State the problem:** Solve the equation $x^2 - y^2 = z^2$ for one of the variables or analyze its structure. 2. **Recognize the formula:** The equation resembles a difference of squares on the left side: $$x^2 - y^2 = (x - y)(x + y)$$ 3. **Rewrite the equation:** Using the difference of squares factorization, we have: $$ (x - y)(x + y) = z^2 $$ 4. **Interpretation:** This means the product of $(x - y)$ and $(x + y)$ equals a perfect square $z^2$. 5. **Solving for $z$:** Taking the square root of both sides: $$ z = \pm \sqrt{(x - y)(x + y)} $$ 6. **Solving for $x$:** Rearranging the original equation: $$ x^2 = y^2 + z^2 $$ Taking the square root: $$ x = \pm \sqrt{y^2 + z^2} $$ 7. **Solving for $y$:** Similarly, $$ y^2 = x^2 - z^2 $$ $$ y = \pm \sqrt{x^2 - z^2} $$ **Summary:** The equation $x^2 - y^2 = z^2$ can be factored and solved for any variable in terms of the others using square roots. The key formula is the difference of squares: $$x^2 - y^2 = (x - y)(x + y)$$