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Let's simplify the given expression step by step. The expression is:

\[
(6x^2 - 7x + 8) - (2x^2 - x + 7) + (4x^2 + 3x - 4)
\]

### Step 1: Distribute the negative sign to the second set of parentheses.

\[
(6x^2 - 7x + 8) - 2x^2 + x - 7 + (4x^2 + 3x - 4)
\]

### Step 2: Now, simplify by removing the parentheses and combining like terms.

For \(x^2\) terms:
\[
6x^2 - 2x^2 + 4x^2 = 8x^2
\]

For \(x\) terms:
\[
-7x + x + 3x = -3x
\]

For constant terms:
\[
8 - 7 - 4 = -3
\]

### Final Expression:

\[
8x^2 - 3x - 3
\]

This is the simplified form of the expression.

Let me know if you'd like more details or have any questions!

### Related Questions:
1. How do you combine like terms in algebraic expressions?
2. What is the importance of distributing the negative sign in expressions?
3. Can you simplify more complex algebraic expressions with different powers?
4. How can this process be applied to polynomials with more terms?
5. How do we solve an equation if the expression equals zero?

### Tip:
Always remember to distribute negative signs carefully when simplifying expressions. It’s easy to make mistakes if you overlook them!

(6x^2 - 7x + 8) - (2x^2 - x + 7) + (4x^2 + 3x - 4)

Learn how to simplify the polynomial expression (6x^2 - 7x + 8) - (2x^2 - x + 7) + (4x^2 + 3x - 4) with a detailed step-by-step solution. This problem covers key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 8-10.

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