-3 · -u · -7v + 8v - 6uv

To simplify the expression -3 · -u · -7v + 8v - 6uv, we can apply the rules of multiplication and combine like terms.

First, let's think about the rules of multiplication:

- When multiplying two negative numbers, the result is positive.
- When multiplying a negative number by a positive number, the result is negative.
- When multiplying two positive numbers, the result is positive.

Now, let's simplify the expression step by step:

1. Multiply -3, -u, and -7v: (-3) · (-u) · (-7v) = 3uv · 7v = 21uv^2

2. Simplify the next term: 8v

3. Multiply -6uv: (-6uv) = -6u · v = -6uv

Now, we can combine the simplified terms:

21uv^2 + 8v - 6uv

This simplified expression is the final answer.