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Let's solve the given expression:

\[
\text{Simplify: } \left(-x + 2 + 4x^2 \right) - \left(-x - 6 - 6x^3 \right)
\]

### Step 1: Remove the parentheses
To simplify the expression, first remove the parentheses by distributing the subtraction across the second group:

\[
- x + 2 + 4x^2 - (-x - 6 - 6x^3)
\]

Distribute the negative sign to each term in the second group:

\[
- x + 2 + 4x^2 + x + 6 + 6x^3
\]

### Step 2: Combine like terms
Now, combine the like terms:

- Combine the \( x \) terms: \( -x + x = 0 \)
- The constant terms: \( 2 + 6 = 8 \)
- The \( x^2 \) term remains \( 4x^2 \)
- The \( x^3 \) term is \( 6x^3 \)

Thus, the simplified expression is:

\[
6x^3 + 4x^2 + 8
\]

This is the final simplified expression. Let me know if you have any questions or if you need more details.

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Here are some related questions you might find interesting:
1. How do you factor a polynomial like \(6x^3 + 4x^2 + 8\)?
2. What are the steps to differentiate the polynomial \(6x^3 + 4x^2 + 8\)?
3. How would you solve \(6x^3 + 4x^2 + 8 = 0\)?
4. Can you graph the polynomial \(6x^3 + 4x^2 + 8\)? What are its key features?
5. How do the degrees of each term affect the shape of the graph of \(6x^3 + 4x^2 + 8\)?

**Tip:** When simplifying expressions with multiple terms, it's crucial to carefully distribute negative signs to ensure accuracy.

Simplify the expression: ( -x + 2 + 4x^2 ) - ( -x - 6 - 6x^3 )

Learn how to simplify the polynomial expression ( -x + 2 + 4x^2 ) - ( -x - 6 - 6x^3 ) step by step. This problem involves the use of the distributive property and combining like terms, essential concepts in algebra for students in Grades 8-10.

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