https://file.aiquickdraw.com/mathbot/file/1727712053556cyc6uu86.jpg

The given expression is:

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

Let's simplify this step by step.

### Step 1: Remove the parentheses
Distribute the negative sign across the second set of parentheses:
\[
3x^2 + x + 4 - 8x + x^2 - x + 7
\]

### Step 2: Combine like terms
- For \(x^2\): \(3x^2 + x^2 = 4x^2\)
- For \(x\): \(x - 8x - x = -8x\)
- For constants: \(4 + 7 = 11\)

### Final simplified expression:
\[
4x^2 - 8x + 11
\]

This is the simplified expression in standard form.

Let me know if you need further clarification!

### Related questions:
1. How do you combine like terms in an algebraic expression?
2. What does distributing a negative sign across parentheses mean?
3. Why is it important to write expressions in standard form?
4. What is the degree of the polynomial \(4x^2 - 8x + 11\)?
5. How would you factor a quadratic expression like \(4x^2 - 8x + 11\)?

### Tip:
When simplifying expressions, always pay attention to negative signs, especially when distributing them across terms inside parentheses!

Learn how to simplify the polynomial expression (3x^2 + x + 4) - (8x - x^2 + x - 7) by combining like terms. This problem covers key algebraic concepts, including simplifying expressions and polynomials. Suitable for students in Grades 7-9.

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