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Let's simplify the given expression:

\[ 4y^3 + 2y^2 - 2y^2 - 2 - 3y - 3y \]

### Step-by-step simplification:
1. Combine like terms:
   - For \( y^3 \), there's only \( 4y^3 \).
   - For \( y^2 \), we have \( 2y^2 - 2y^2 \), which cancels out to 0.
   - For \( y \), we have \( -3y - 3y = -6y \).
   - The constant term is \( -2 \).

Thus, the simplified expression is:

\[ 4y^3 - 6y - 2 \]

This matches the first option:
\[ \boxed{4y^3 - 6y - 2} \]

Would you like more details on any step or have any other questions?

Here are 5 related questions to deepen your understanding:
1. How do you combine like terms in polynomials?
2. Why did the \( 2y^2 - 2y^2 \) terms cancel out?
3. How would you factor \( 4y^3 - 6y - 2 \)?
4. Can this expression be factored further to find roots?
5. What would happen if additional terms like \( +5 \) were included?

**Tip:** Always look for like terms first when simplifying algebraic expressions, as this often makes the problem much easier.

Simplify 4y^3 + 2y^2 - 2y^2 - 2 - 3y - 3y.

Learn how to simplify the polynomial expression 4y^3 + 2y^2 - 2y^2 - 2 - 3y - 3y step-by-step. This problem covers key algebraic concepts such as combining like terms and simplifying polynomials. Suitable for students in Grades 7-9.

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