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

Let's simplify the expression step by step:

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

1. First, distribute the negative signs:
\[
7x^2 - 6x + 2 - 4x + 8 - 6x^2 + 3x
\]

2. Now, combine like terms:

- \(7x^2\) and \(-6x^2\):  
\[
7x^2 - 6x^2 = x^2
\]

- \(-6x\), \(-4x\), and \(3x\):  
\[
-6x - 4x + 3x = -7x
\]

- Constants \(2\) and \(8\):  
\[
2 + 8 = 10
\]

So, the simplified expression is:
\[
x^2 - 7x + 10
\]

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

Here are some related questions for further practice:
1. How do you factor a quadratic expression like \(x^2 - 7x + 10\)?
2. Can you find the roots of \(x^2 - 7x + 10\)?
3. How do you complete the square for \(x^2 - 7x + 10\)?
4. What is the discriminant of \(x^2 - 7x + 10\) and what does it tell you?
5. How would the expression change if a term was raised to a higher degree (e.g., \(x^3\))?

**Tip:** Always double-check for like terms when simplifying complex expressions; it helps avoid mistakes!

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

Learn how to simplify the polynomial expression (7x^2 - 6x + 2) - (4x - 8) + (-6x^2 + 3x) by distributing negative signs and combining like terms. This step-by-step solution is suitable for students in Grades 7-9.

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