8) \( \frac{(p-q)^{2}}{(q-p)^{2}} \)

Did you know that \( (p-q) \) and \( (q-p) \) are essentially opposites? What this means is that when you square them, those negative signs vanish! So in essence, \( \frac{(p-q)^{2}}{(q-p)^{2}} = \frac{(p-q)^{2}}{(-1)^{2}(p-q)^{2}} = 1 \). Also, this expression is a fabulous example of how algebra can simplify concepts. By recognizing patterns like this, students can save a lot of time on tests. Instead of getting caught up in lengthy calculations, identify relationships and use symmetry to reach the answer quickly. It’s like finding a shortcut through a maze!