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The expression to simplify is:

\[
(6x^2 - 2x + 3) + (-7x^2 + 4x + 1)
\]

Now, let's simplify it step by step:

1. **Group the like terms**:
   \[
   (6x^2 - 7x^2) + (-2x + 4x) + (3 + 1)
   \]

2. **Combine the like terms**:
   - For the \(x^2\) terms: \(6x^2 - 7x^2 = -x^2\)
   - For the \(x\) terms: \(-2x + 4x = 2x\)
   - For the constants: \(3 + 1 = 4\)

3. **Write the simplified expression**:
   \[
   -x^2 + 2x + 4
   \]

So, the simplified form of the expression is:
\[
-x^2 + 2x + 4
\]

Would you like more details on any part of this process, or do you have any questions?

Here are 5 related questions for deeper understanding:
1. How do you identify and group like terms in a polynomial?
2. What are the steps to simplify an expression with parentheses?
3. Can you explain how to combine negative and positive terms?
4. How does the degree of a polynomial change after simplifying?
5. What is the significance of the order when writing simplified expressions?

**Tip:** Always start by simplifying the highest-degree terms in a polynomial to keep track of your work more clearly.

Simplify (6x^2 - 2x + 3) + (-7x^2 + 4x + 1)

Learn how to simplify the polynomial expression (6x^2 - 2x + 3) + (-7x^2 + 4x + 1). This solution includes step-by-step guidance on combining like terms and applying basic algebraic principles. Suitable for students in Grades 8-10.

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