The task involves solving two addition and subtraction problems with polynomials. Here are the given expressions:

1. $(2k^2 - 3k + 2) + (-3k^2 - 3k + 2)$
2. $(3x^2 - 2x + 3) - (2x^2 + 4)$

Let’s solve them step-by-step.

Problem 1:

$(2k^2 - 3k + 2) + (-3k^2 - 3k + 2)$

1. Combine like terms:
   • $2k^2 - 3k^2 = -k^2$
   • $-3k - 3k = -6k$
   • $2 + 2 = 4$

Solution: $- k^2 - 6k + 4$

Problem 2:

$(3x^2 - 2x + 3) - (2x^2 + 4)$

1. Distribute the negative sign to the second polynomial: $3x^2 - 2x + 3 - 2x^2 - 4$

2. Combine like terms:

   • $3x^2 - 2x^2 = x^2$
   • $-2x$ (no similar term to combine)
   • $3 - 4 = -1$

Solution: $x^2 - 2x - 1$

Final Answers:

1. $-k^2 - 6k + 4$
2. $x^2 - 2x - 1$

Would you like me to break down any step in more detail?

Related Questions:

1. How do you add and subtract polynomials with more variables?
2. What does it mean to simplify a polynomial expression?
3. Can subtraction between polynomials introduce errors if not distributed correctly?
4. How do the degree and leading term of a polynomial affect addition and subtraction?
5. What strategies can be used to double-check polynomial arithmetic?

Tip:

Always align terms with the same degree (e.g., $x^2$ with $x^2$) when performing addition or subtraction to avoid mistakes.