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The given expression is:

\[
(10x + 10) - (7x^2 + 5x - 8)
\]

Let's simplify this step by step:

### Step 1: Distribute the negative sign across the second parentheses
\[
= 10x + 10 - 7x^2 - 5x + 8
\]

### Step 2: Combine like terms
- \(10x - 5x = 5x\)
- \(10 + 8 = 18\)
- No like terms for \(7x^2\)

Thus, the simplified expression is:

\[
-7x^2 + 5x + 18
\]

This is the result of performing the operation.

Would you like further details or have any questions?

Here are 5 related questions to extend your understanding:
1. How do you simplify expressions with parentheses?
2. What happens if both parentheses contain negative signs?
3. Can you add or subtract expressions with different powers of \(x\)?
4. How does this simplification change if you multiply both terms by a constant?
5. What are common errors when distributing negative signs?

**Tip:** Always distribute negative signs carefully to avoid sign errors when simplifying expressions!

Discover how to simplify the polynomial expression (10x + 10) - (7x^2 + 5x - 8) by distributing negative signs and combining like terms. This step-by-step guide is suitable for students in grades 8 to 10, covering key algebraic concepts and practices.

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