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!