Answer :

Sure! Let's go step-by-step to simplify the given expression:

[tex]\(7mn(2m^2 - 4n^2 + 2) + mn(m^2 - n^2)\)[/tex]

### Step 1: Distribute [tex]\(mn\)[/tex] inside the parentheses

First, distribute [tex]\(7mn\)[/tex] inside the first parentheses:
[tex]\[7mn(2m^2) - 7mn(4n^2) + 7mn(2)\][/tex]
[tex]\[= 14m^3n - 28mn^3 + 14mn\][/tex]

Now distribute [tex]\(mn\)[/tex] inside the second parentheses:
[tex]\[mn(m^2) - mn(n^2)\][/tex]
[tex]\[= m^3n - mn^3\][/tex]

### Step 2: Combine like terms

Now we have:
[tex]\[14m^3n - 28mn^3 + 14mn + m^3n - mn^3\][/tex]

Combine the terms:
1. [tex]\(m^3n\)[/tex] terms:
[tex]\[14m^3n + m^3n = 15m^3n\][/tex]

2. [tex]\(mn^3\)[/tex] terms:
[tex]\[-28mn^3 - mn^3 = -29mn^3\][/tex]

3. [tex]\(mn\)[/tex] terms:
[tex]\[14mn\][/tex]

### Step 3: Write the final simplified expression:
[tex]\[ 15m^3n - 29mn^3 + 14mn \][/tex]

So, the simplified form of the given expression is:

[tex]\[ 15m^3n - 29mn^3 + 14mn \][/tex]