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Evaluate the following expression. Choose the correct answer among the given choices.

Let's simplify the given expression:

\[
(3x^2 - 2x + 1) - (4x^2 + 5x - 3)
\]

To simplify this, we need to distribute the negative sign across the second expression and then combine like terms.

1. Distribute the negative sign:

\[
3x^2 - 2x + 1 - 4x^2 - 5x + 3
\]

2. Combine like terms:

   - For \(x^2\): \(3x^2 - 4x^2 = -x^2\)
   - For \(x\): \(-2x - 5x = -7x\)
   - For the constants: \(1 + 3 = 4\)

So, the simplified expression is:

\[
-x^2 - 7x + 4
\]

Now, let's check which option matches this expression. The correct answer is:

**A) \(-x^2 - 7x + 4\)**

Would you like any further details or explanations?

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Here are some related questions for further practice:

1. How would you simplify the expression \((5x^2 + 4x - 2) - (2x^2 - x + 3)\)?
2. What is the result of subtracting \((6x^2 + 7x + 5)\) from \((8x^2 - 4x - 1)\)?
3. If the expression was \((4x^2 - 3x + 2) + (3x^2 + x - 5)\), what would the simplified form be?
4. How do you expand and simplify \((2x - 3)(x + 4)\)?
5. What is the general approach to simplifying expressions involving polynomials?

**Tip:** Always distribute negative signs carefully when subtracting polynomials to avoid errors in combining like terms.

Learn how to evaluate the expression (3x^2 - 2x + 1) - (4x^2 + 5x - 3) step-by-step. Simplify by distributing and combining like terms. Suitable for high school students studying polynomials and algebraic expressions.

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