https://file.aiquickdraw.com/mathbot/file/1727712214727mjhtipxu.jpg

The expression given in the image is:

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

Let's simplify this step by step:

1. **Distribute the negative sign** across the terms inside the parentheses:
   \[
   3x^2 + x + 4 - (8x - x^2 + x - 7)
   = 3x^2 + x + 4 - 8x + x^2 - x + 7
   \]

2. **Combine like terms**:
   - \( 3x^2 + x^2 = 4x^2 \)
   - \( x - 8x - x = -8x \)
   - \( 4 + 7 = 11 \)

Thus, the simplified expression is:

\[
4x^2 - 8x + 11
\]

This is the expression in standard form.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. How do you distribute a negative sign across multiple terms inside parentheses?
2. What are "like terms," and why is combining them important in simplification?
3. How would the expression change if the negative sign were in front of the entire first set of parentheses?
4. Can you factor the final expression \(4x^2 - 8x + 11\)?
5. How would this expression change if we were solving it as an equation set equal to 0?

**Tip**: When combining like terms, always keep an eye on the coefficients and signs to avoid mistakes.

Learn how to simplify the polynomial expression (3x^2 + x + 4) - (8x - x^2 + x - 7) step-by-step. This algebra problem covers concepts such as the distributive property and combining like terms, suitable for students in Grades 7-9.

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