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Ayudame hallar las sumas de los POLINOMIOS paso a paso MATEMATICAS

Let's go through the sums of these polynomials step by step for each given set.

### 7. First Set: \( -7x - 4y + 6z \), \( 10x - 20y - 8z \), and \( -5x + 24y + 2z \)
- Combine like terms:
  \[
  (-7x - 4y + 6z) + (10x - 20y - 8z) + (-5x + 24y + 2z) = -7x + 10x - 5x - 4y - 20y + 24y + 6z - 8z + 2z
  \]
- Simplify:
  \[
  = -2x + 0y + 0z = -2x
  \]
  (The \(y\) and \(z\) terms cancel each other out.)

### 8. Second Set: \( -2m + 3n - 6 \), \( 3m - 8n + 8 \), and \( -5m + n - 10 \)
- Combine like terms:
  \[
  (-2m + 3n - 6) + (3m - 8n + 8) + (-5m + n - 10) = -2m + 3m - 5m + 3n - 8n + n - 6 + 8 - 10
  \]
- Simplify:
  \[
  = -4m - 4n - 8
  \]

### 9. Third Set: \( -5a - 2b - 3c \), \( 7a - 3b + 5c \), and \( -8a + 5b - 3c \)
- Combine like terms:
  \[
  (-5a - 2b - 3c) + (7a - 3b + 5c) + (-8a + 5b - 3c) = -5a + 7a - 8a - 2b - 3b + 5b - 3c + 5c - 3c
  \]
- Simplify:
  \[
  = -6a + 0b - 1c = -6a - c
  \]
  (The \(b\) terms cancel each other out.)

### 10. Fourth Set: \( ab + bc + cd \), \( -8ab - 3bc - 3cd \), and \( 5ab + 2bc + 2cd \)
- Combine like terms:
  \[
  (ab + bc + cd) + (-8ab - 3bc - 3cd) + (5ab + 2bc + 2cd) = ab - 8ab + 5ab + bc - 3bc + 2bc + cd - 3cd + 2cd
  \]
- Simplify:
  \[
  = -2ab + 0bc + 0cd = -2ab
  \]
  (The \(bc\) and \(cd\) terms cancel each other out.)

### 11. Fifth Set: \( ax - ay - az \), \( -5ax - 7ay - 6az \), and \( 6ax + 9ay + 8az \)
- Combine like terms:
  \[
  (ax - ay - az) + (-5ax - 7ay - 6az) + (6ax + 9ay + 8az) = ax - 5ax + 6ax - ay - 7ay + 9ay - az - 6az + 8az
  \]
- Simplify:
  \[
  = 2ax + ay + az
  \]

### 12. Sixth Set: \( 5x - 7y + 8 \), \( -y + 6 - 4x \), and \( 9 - 3x + 8y \)
- Combine like terms:
  \[
  (5x - 7y + 8) + (-y + 6 - 4x) + (9 - 3x + 8y) = 5x - 4x - 3x - 7y - y + 8y + 8 + 6 + 9
  \]
- Simplify:
  \[
  = -2x + 0y + 23 = -2x + 23
  \]
  (The \(y\) terms cancel each other out.)

### Summary:
- First Set: \( -2x \)
- Second Set: \( -4m - 4n - 8 \)
- Third Set: \( -6a - c \)
- Fourth Set: \( -2ab \)
- Fifth Set: \( 2ax + ay + az \)
- Sixth Set: \( -2x + 23 \)

Would you like further clarification on any of these steps, or do you have any other questions?

### Related Questions:
1. How do you multiply polynomials with multiple terms and variables?
2. How do you factor polynomials after addition?
3. What is the significance of the degree of a polynomial in addition?
4. How do you perform polynomial division?
5. Can you apply polynomial identities to simplify expressions before adding them?

### Tip:
Always double-check your work by re-adding the terms after simplifying, ensuring that no terms are accidentally omitted or incorrectly combined.

Explore step-by-step solutions for adding polynomials with detailed explanations. Learn how to combine like terms and simplify expressions effectively. Suitable for high school students studying polynomial addition.

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