Factor \( n^{3}-q_{n} \)

To factor \( n^{3} - q_{n} \), you can use the difference of cubes formula. The difference of cubes states that \( a^{3} - b^{3} = (a-b)(a^{2} + ab + b^{2}) \). In this case, let’s take \( a = n \) and \( b = q_{n} \). Applying the formula gives us: \( n^{3} - q_{n} = (n - q_{n})(n^{2} + n q_{n} + q_{n}^{2}) \). So, you've effectively factored \( n^{3} - q_{n} \) into two parts! In mathematical terms, factoring can seem daunting at first, but with practice, it becomes second nature! Always look for patterns, and don’t hesitate to use identity formulas like the difference of cubes or the ones for squares. Remember, even if a problem looks complex, breaking it down into simpler components can reveal the factors hiding beneath the surface!