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!