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Let's go through the addition and subtraction of the given expressions one by one.

1. **(3x + 2) + (4x + 6)**:
   \[
   (3x + 2) + (4x + 6) = 3x + 4x + 2 + 6 = 7x + 8
   \]

2. **(2x + y + 3z) + (x - y + z)**:
   \[
   (2x + y + 3z) + (x - y + z) = 2x + x + y - y + 3z + z = 3x + 4z
   \]

3. **(x^2 + 2) + (x^2 - 5)**:
   \[
   (x^2 + 2) + (x^2 - 5) = x^2 + x^2 + 2 - 5 = 2x^2 - 3
   \]

4. **(3a^2 + 2a - 1) + (a^2 + a + 1)**:
   \[
   (3a^2 + 2a - 1) + (a^2 + a + 1) = 3a^2 + a^2 + 2a + a - 1 + 1 = 4a^2 + 3a
   \]

5. **(2x^2 + 3x - 1) + (x^2 - x + 2)**:
   \[
   (2x^2 + 3x - 1) + (x^2 - x + 2) = 2x^2 + x^2 + 3x - x - 1 + 2 = 3x^2 + 2x + 1
   \]

6. **(2z - z^2 + 5) + (z^2 - 3z + 1)**:
   \[
   (2z - z^2 + 5) + (z^2 - 3z + 1) = 2z - z^2 + z^2 - 3z + 5 + 1 = -z + 6
   \]

7. **(3 - 2t^2 + t) + (t^2 - t - 3)**:
   \[
   (3 - 2t^2 + t) + (t^2 - t - 3) = 3 - 2t^2 + t + t^2 - t - 3 = -t^2
   \]

These are the simplified results of the given problems.

Would you like further details or explanations on any specific problem?

Here are 5 related questions to expand your understanding:
1. How do you combine like terms in algebraic expressions?
2. What is the difference between addition and subtraction of polynomials?
3. Can you apply these principles to expressions with higher powers of variables?
4. How do negative signs affect combining terms across parentheses?
5. What role do constants play in simplifying polynomial expressions?

**Tip:** Always align similar powers of variables when combining terms to avoid mistakes during addition or subtraction.

Add or subtract the given polynomial expressions.

This lesson covers how to add and subtract polynomial expressions, including terms with multiple variables. Example problems simplify expressions like (3x + 2) + (4x + 6) and (2x + y + 3z) + (x - y + z), suitable for students in Grades 7-9.

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