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To solve the sum of polynomials step by step, let's go through each set of expressions one by one. The task is to add the polynomials within each set.

### 1. First Set: \( 3a + 2b - c \) and \( 2a + 3b + c \)
- Combine like terms:
  \[
  (3a + 2b - c) + (2a + 3b + c) = 3a + 2a + 2b + 3b - c + c
  \]
- Simplify:
  \[
  = 5a + 5b
  \]

### 2. Second Set: \( 7a - 4b + 5c \) and \(-7a + 4b - 6c \)
- Combine like terms:
  \[
  (7a - 4b + 5c) + (-7a + 4b - 6c) = 7a - 7a - 4b + 4b + 5c - 6c
  \]
- Simplify:
  \[
  = -c
  \]

### 3. Third Set: \( m + n - p \) and \( -m - n + p \)
- Combine like terms:
  \[
  (m + n - p) + (-m - n + p) = m - m + n - n - p + p
  \]
- Simplify:
  \[
  = 0
  \]
  (All terms cancel each other out.)

### 4. Fourth Set: \( 9x - 3y + 5 \), \( -x - y + 4 \), and \( -5x + 4y - 9 \)
- Combine like terms:
  \[
  (9x - 3y + 5) + (-x - y + 4) + (-5x + 4y - 9) = 9x - x - 5x - 3y - y + 4y + 5 + 4 - 9
  \]
- Simplify:
  \[
  = 3x + 0y = 3x
  \]
  (The \(y\) terms cancel each other out.)

### 5. Fifth Set: \( a + b - c \), \( 2a + 2b - 2c \), and \( -3a - b + 3c \)
- Combine like terms:
  \[
  (a + b - c) + (2a + 2b - 2c) + (-3a - b + 3c) = a + 2a - 3a + b + 2b - b - c - 2c + 3c
  \]
- Simplify:
  \[
  = 0
  \]
  (All terms cancel each other out.)

### 6. Sixth Set: \( p + q + r \), \( -2p - 6q + 3r \), and \( p + 5q - 8r \)
- Combine like terms:
  \[
  (p + q + r) + (-2p - 6q + 3r) + (p + 5q - 8r) = p - 2p + p + q - 6q + 5q + r + 3r - 8r
  \]
- Simplify:
  \[
  = 0
  \]
  (All terms cancel each other out.)

### Summary:
- First Set: \( 5a + 5b \)
- Second Set: \( -c \)
- Third Set: \( 0 \)
- Fourth Set: \( 3x \)
- Fifth Set: \( 0 \)
- Sixth Set: \( 0 \)

Would you like more detailed steps for any of these calculations, or do you have any other questions?

### Related Questions:
1. How do you handle the addition of polynomials with more than three terms?
2. What happens when polynomials contain more variables?
3. How do you subtract polynomials?
4. How do you multiply polynomials with multiple variables?
5. How can polynomial identities be used to simplify algebraic expressions?

### Tip:
Always align like terms (same variable and power) vertically or clearly mark them before performing addition or subtraction to avoid mistakes.

Discover how to add polynomials step by step with detailed examples. This guide covers combining like terms and simplifying expressions, essential for understanding polynomial addition. Suitable for high school students.

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