Answer :

To solve the expression [tex]\(-7mn - [-3mn - (4mn - 2mn)]\)[/tex], we'll work step-by-step, simplifying the innermost parentheses first and gradually moving outward. Here's the detailed solution:

1. Simplify the innermost parentheses:
[tex]\[ 4mn - 2mn \][/tex]
Since both terms have the same variables [tex]\(mn\)[/tex], we can simply subtract the coefficients:
[tex]\[ (4-2)mn = 2mn \][/tex]

Now the expression is:
[tex]\[ -7mn - [-3mn - 2mn] \][/tex]

2. Simplify the middle parentheses:
[tex]\[ -3mn - 2mn \][/tex]
Again, combining the like terms:
[tex]\[ (-3 - 2)mn = -5mn \][/tex]

Now the expression is:
[tex]\[ -7mn - (-5mn) \][/tex]

3. Simplify the outer expression:
[tex]\(-(-5mn)\)[/tex] becomes [tex]\(+5mn\)[/tex]. Thus the expression simplifies to:
[tex]\[ -7mn + 5mn \][/tex]

Finally, combining the like terms:
[tex]\[ (-7 + 5)mn = -2mn \][/tex]

So, the simplified expression is:
[tex]\[ -2mn \][/tex]