a) \( \begin{array}{c}8 y-16 y^{2} \\ 4 y^{2}\end{array} \)

To simplify the expression \( \frac{8y - 16y^{2}}{4y^{2}} \), you can start by factoring the numerator. Notice that you can factor out \( 8y \) from the numerator, giving you \( 8y(1 - 2y) \). Now your expression looks like \( \frac{8y(1 - 2y)}{4y^{2}} \). You can simplify this further by dividing both the numerator and denominator by \( 4y \) (assuming \( y \neq 0 \)), which results in \( \frac{2(1 - 2y)}{y} \). Let's break this down: you're left with \( \frac{2 - 4y}{y} \), which can be rewritten as \( 2/y - 4 \). Voilà! A more manageable fraction. If you encounter this type of expression, remember to always look for common factors to factor out first. One common mistake might be neglecting to factor completely or forgetting to cancel out terms, so keep an eye on that!