Expand

To expand the expression \( \frac{5}{8}(-8 - 3f) \), we will distribute \( \frac{5}{8} \) to both terms inside the parentheses.

1. Distributing \( \frac{5}{8} \) to \(-8\): \[ \frac{5}{8} \times -8 = -\frac{40}{8} = -5 \]

2. Distributing \( \frac{5}{8} \) to \(-3f\): \[ \frac{5}{8} \times -3f = -\frac{15}{8}f \]

Now combine the two results:

\[ \frac{5}{8}(-8 - 3f) = -5 - \frac{15}{8}f \]

This can be rearranged as:

\[ -\frac{15}{8}f - 5 \]

Now, looking at the options provided: A. \( \frac{15}{8}f - 5 \)
B. \( \frac{15}{8}f + 5 \)
C. \( -\frac{15}{8}f - 5 \)
D. \( -\frac{15}{8} + 5 \)

The correct answer is:

C. \( -\frac{15}{8}f - 5 \)