Answer :

Certainly! Let's go through the given expression step by step:

The original expression to simplify is:
[tex]\[ \left(4 m^2 + 14 m^3 n\right) - \left(-m n^3 - 4 m^3 n - 11 m^2\right) - \left(m n^3 - 13 m^2\right) \][/tex]

### Step 1: Distribute the negative signs
First, let's distribute the negative signs across the terms inside the parentheses.

[tex]\[ \left(4 m^2 + 14 m^3 n\right) - \left(-m n^3 - 4 m^3 n - 11 m^2\right) - \left(m n^3 - 13 m^2\right) \][/tex]

Becomes:

[tex]\[ 4 m^2 + 14 m^3 n + m n^3 + 4 m^3 n + 11 m^2 - m n^3 + 13 m^2 \][/tex]

### Step 2: Combine like terms
Now, we combine all like terms. The like terms include [tex]\(m^2\)[/tex], [tex]\(m^3n\)[/tex], and [tex]\(mn^3\)[/tex]:

- [tex]\(m^2\)[/tex] terms: [tex]\(4 m^2 + 11 m^2 + 13 m^2\)[/tex]
- [tex]\(m^3 n\)[/tex] terms: [tex]\(14 m^3 n + 4 m^3 n\)[/tex]
- [tex]\(m n^3\)[/tex] terms: [tex]\(m n^3 - m n^3\)[/tex]

Combining these, we get:

[tex]\[ (4 + 11 + 13)m^2 + (14 + 4) m^3 n + (1 - 1) m n^3 \][/tex]

Simplifying each group of terms, we get:

[tex]\[ 28 m^2 + 18 m^3 n + 0 m n^3 \][/tex]

### Step 3: Simplify the expression
Since [tex]\(0 m n^3\)[/tex] is zero, we can remove that term, leaving us with:

[tex]\[ 28 m^2 + 18 m^3 n \][/tex]

### Step 4: Factor out the greatest common factor
Lastly, we factor out the greatest common factor from [tex]\(28 m^2 + 18 m^3 n\)[/tex]. The greatest common factor is [tex]\(2 m^2\)[/tex]:

[tex]\[ 28 m^2 + 18 m^3 n = 2 m^2 (14) + 2 m^2 (9 m n) \][/tex]

Thus, the simplified form is:

[tex]\[ 10 m^2 (m n - 2) \][/tex]

### Conclusion
The simplified expression is:
[tex]\[ \boxed{10 m^2 (m n - 2)} \][/tex]