Let's simplify the given expression:

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

### Step 1: Distribute the negative sign to the second parenthesis
\[
(3 - 2x^2) - x^2 - 6 + 2x
\]

### Step 2: Combine like terms

- For \(x^2\) terms: \(-2x^2 - x^2 = -3x^2\)
- For constant terms: \(3 - 6 = -3\)
- For \(x\) terms: \(2x\)

### Final expression:
\[
-3x^2 + 2x - 3
\]

This is the simplified form of the expression.

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you simplify a similar expression with cubic terms?
2. Can you factor the quadratic expression \(-3x^2 + 2x - 3\)?
3. What is the vertex of the parabola represented by \(-3x^2 + 2x - 3\)?
4. How do you complete the square for \(-3x^2 + 2x - 3\)?
5. How would this expression change if an additional term, say \(4x\), were added?

**Tip:** Always double-check your distribution of negative signs to avoid mistakes!

Learn how to simplify the polynomial expression (3 - 2x^2) - (x^2 + 6 - 2x) with a detailed step-by-step solution. This problem covers key algebraic concepts, such as the distributive property and combining like terms. Suitable for students in Grades 8-10.

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