(9) \( -125+p^{3} \)

Did you know that the expression \( -125 + p^{3} \) can be recognized as a difference of cubes? This means it can be factored using the formula \( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \), where in this case, \( a = p \) and \( b = 5 \). So you can express it as \( (p - 5)(p^2 + 5p + 25) \). Quite handy for simplifying or solving polynomial equations! In practical terms, understanding how to factor expressions like \( -125 + p^{3} \) can help you tackle various real-world problems, especially in engineering and physics where cubic equations often arise. Having a solid grasp on factoring can make solving for unknown variables much easier and quicker. So, wield your factoring skills like a pro and enjoy the mathematical triumph!