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Let's simplify the expression provided:

\[
(-5v^3 - 9v^2 + 6v) - (-5v^3 + 9v^2 - 6v)
\]

First, distribute the negative sign across the second set of parentheses:

\[
-5v^3 - 9v^2 + 6v + 5v^3 - 9v^2 + 6v
\]

Next, combine like terms:

- Combine the \(v^3\) terms: \(-5v^3 + 5v^3 = 0\)
- Combine the \(v^2\) terms: \(-9v^2 - 9v^2 = -18v^2\)
- Combine the \(v\) terms: \(6v + 6v = 12v\)

So, the simplified expression is:

\[
-18v^2 + 12v
\]

Would you like more details or have any questions about this simplification? Here are some related questions:

1. How do you simplify algebraic expressions with multiple terms?
2. What is the role of distribution in simplifying expressions?
3. How do you combine like terms in an algebraic expression?
4. Can this expression be factored further?
5. How would the simplification change if different coefficients were used?

**Tip:** Always be careful when distributing negative signs, as this is a common place where errors can occur.

Learn how to simplify the expression -5v^3 - 9v^2 + 6v - (-5v^3 + 9v^2 - 6v) step-by-step. This problem covers key algebraic concepts such as simplifying expressions and combining like terms. Suitable for students in Grades 7-9.

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