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]
