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To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we start by distributing the minus sign across the terms in the second parenthesis:

\[
(9x^2 - 6x + 2) - x^2 - 4x + 39
\]

Now, we combine like terms:
- The \(x^2\) terms: \(9x^2 - x^2 = 8x^2\),
- The \(x\) terms: \(-6x - 4x = -10x\),
- The constant terms: \(2 + 39 = 41\).

So, the expression simplifies to:

\[
8x^2 - 10x + 41
\]

This is the simplified form of the original expression. If you have any further questions or need more details, feel free to ask!

Here are some related questions to consider:
1. What would the expression be if you factorized it?
2. How would you find the roots of the equation \(8x^2 - 10x + 41 = 0\)?
3. Can you plot the graph of the function \(y = 8x^2 - 10x + 41\)?
4. What is the vertex of the parabola described by \(y = 8x^2 - 10x + 41\)?
5. How would you determine the concavity of the graph of \(y = 8x^2 - 10x + 41\)?

**Tip:** Always check your final expression by substituting a few values of \(x\) to see if it agrees with the original expression at those points. This can help confirm the correctness of your simplification.

Simplify (9x^2 - 6x + 2) - (x^2 + 4x - 39).

Learn how to simplify the polynomial expression (9x^2 - 6x + 2) - (x^2 + 4x - 39) by distributing the negative sign and combining like terms. This problem covers key algebraic concepts, including simplification and combining polynomials. Suitable for students in Grades 7-9.

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