Let's simplify the given expression:

\[
(3x^2 - 2x + 4) - (x^2 - x - 1)
\]

1. Distribute the negative sign across the second parentheses:
\[
3x^2 - 2x + 4 - x^2 + x + 1
\]

2. Combine like terms:
   - \(3x^2 - x^2 = 2x^2\)
   - \(-2x + x = -x\)
   - \(4 + 1 = 5\)

So the simplified expression is:
\[
2x^2 - x + 5
\]

Let me know if you want further details or have any questions.

Here are some related questions for practice:
1. Simplify: \((4x^2 + 3x - 7) - (2x^2 - x + 5)\)
2. Expand and simplify: \((2x - 3)(x + 4)\)
3. Solve for \(x\): \(2x^2 - x + 5 = 0\)
4. Factor: \(2x^2 - x - 6\)
5. Simplify: \(5(x - 2) - 3(2x + 1)\)

**Tip:** Always distribute negative signs carefully when subtracting polynomials.

This guide walks you through simplifying the polynomial expression (3x^2 - 2x + 4) - (x^2 - x - 1), demonstrating key algebraic techniques like distributing the negative sign and combining like terms. Suitable for students in Grades 8-10.

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