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We are asked to find the expression equivalent to \((7x^2 - 5x + 1) - (x^2 - 3x - 2)\).

### Step-by-step process:
1. **Distribute the negative sign** to the second polynomial:
   \[
   (7x^2 - 5x + 1) - (x^2 - 3x - 2) = 7x^2 - 5x + 1 - x^2 + 3x + 2
   \]
   
2. **Combine like terms**:
   - \(7x^2 - x^2 = 6x^2\)
   - \(-5x + 3x = -2x\)
   - \(1 + 2 = 3\)

So, the simplified expression is:
\[
6x^2 - 2x + 3
\]

### Answer:
The correct choice is **D: 6x² - 2x + 3**.

Let me know if you'd like further clarification!

Here are 5 related questions for practice:
1. What is the result of \((5x^2 + 3x - 4) - (2x^2 - 6x + 3)\)?
2. How do you subtract polynomials with more than three terms?
3. Can you explain how to distribute negative signs in polynomial expressions?
4. What is the simplified form of \((4x^2 + 2x - 7) - (3x^2 + x + 1)\)?
5. How does polynomial subtraction differ from polynomial addition?

**Tip:** Always distribute the negative sign to each term of the second polynomial when subtracting two polynomials!

Which expression is equivalent to (7x^2 - 5x + 1) - (x^2 - 3x - 2)?

Learn how to subtract two polynomials and combine like terms with this detailed explanation of the expression (7x^2 - 5x + 1) - (x^2 - 3x - 2). This lesson covers polynomial subtraction and algebraic manipulation, suitable for students in Grades 8-10.

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