To simplify the expression \(-4(3x - y + 8)\), distribute the \(-4\) to each term inside the parentheses:

\[
-4(3x - y + 8) = -4 \cdot 3x + (-4) \cdot (-y) + (-4) \cdot 8
\]

This gives:

\[
-12x + 4y - 32
\]

So, the simplified expression is \(-12x + 4y - 32\).

Would you like further details or have any questions?

Here are some related questions:

1. How do you distribute a negative number across multiple terms?
2. What if the expression had more variables inside the parentheses?
3. How do you solve equations involving expressions like \(-4(3x - y + 8)\)?
4. Can you factor the simplified expression \(-12x + 4y - 32\)?
5. How does the distribution change if the initial number was positive instead of negative?
6. What happens if you distribute across an expression with fractions?
7. How do you check your work when simplifying expressions like this?
8. How would this expression change if it were \(-5(3x - y + 8)\) instead?

**Tip:** Be mindful of signs when distributing negative numbers to avoid common errors.

Learn how to simplify the expression -4 times the quantity 3x minus y plus 8. This problem covers algebraic concepts such as the distributive property. Suitable for students in Grades 7-9.

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