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AYUDAME A SUMAR POLINOMIO PASO A PASO DE: 

To sum the polynomial, we'll group like terms and simplify step by step. Let's start by identifying the terms in the polynomial:

\[ -7m^2n + 4n^3 + m^3 + 6mn^2 - n^3 - m^3 + 7m^2n + 5n^3 \]

### Step 1: Group like terms
We'll first group the like terms together:

- Terms involving \(m^3\):
  \[ m^3 - m^3 \]

- Terms involving \(m^2n\):
  \[ -7m^2n + 7m^2n \]

- Terms involving \(mn^2\):
  \[ 6mn^2 \] (this term is alone, so it stays as is)

- Terms involving \(n^3\):
  \[ 4n^3 - n^3 + 5n^3 \]

### Step 2: Simplify each group
Now let's simplify each group:

- For the \(m^3\) terms:
  \[ m^3 - m^3 = 0 \]

- For the \(m^2n\) terms:
  \[ -7m^2n + 7m^2n = 0 \]

- For the \(mn^2\) term:
  \[ 6mn^2 \] (no change here)

- For the \(n^3\) terms:
  \[ 4n^3 - n^3 + 5n^3 = (4 - 1 + 5)n^3 = 8n^3 \]

### Step 3: Combine the simplified terms
The simplified polynomial, after combining all the like terms, is:

\[
8n^3 + 6mn^2
\]

So, the sum of the given polynomial is:

\[
8n^3 + 6mn^2
\]

Would you like further details or have any questions?

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Here are 5 related questions that can help deepen your understanding:

1. How do you identify like terms in a polynomial?
2. What are the steps involved in simplifying a polynomial with multiple variables?
3. How do you factor a polynomial after simplifying it?
4. What role does the distributive property play in polynomial addition?
5. How do you handle polynomials with negative coefficients differently?

**Tip:** Always double-check each group of like terms to avoid missing or incorrectly combining terms!

Learn how to sum the polynomial step by step with detailed explanations and examples. This problem covers key concepts in polynomial algebra, including identifying like terms, simplifying polynomials, and combining terms effectively. Suitable for students in Grades 7-9.

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