Sure, let's solve the expression step-by-step.
The given mathematical expression is:
[tex]\[
(7 - 5) \cdot [3 - 2 - 4 \div 2 - 3 \cdot (6 - 2 - 8 \div 4)]
\][/tex]
First, we'll handle the innermost parentheses:
1. Calculate [tex]\(8 \div 4\)[/tex]:
[tex]\[
8 \div 4 = 2
\][/tex]
2. Substitute this result into the expression [tex]\(6 - 2 - 8 \div 4\)[/tex]:
[tex]\[
6 - 2 - 2
\][/tex]
3. Perform the subtraction step by step:
[tex]\[
6 - 2 = 4
\][/tex]
[tex]\[
4 - 2 = 2
\][/tex]
So, the value of the innermost expression is [tex]\(2\)[/tex].
Now substitute this back into the larger expression:
[tex]\[
(7 - 5) \cdot [3 - 2 - 4 \div 2 - 3 \cdot 2]
\][/tex]
Next, simplify the remaining expression inside the brackets:
4. Calculate [tex]\(4 \div 2\)[/tex]:
[tex]\[
4 \div 2 = 2
\][/tex]
5. Substitute this into the expression [tex]\(3 - 2 - 4 \div 2 - 3 \cdot 2\)[/tex]:
[tex]\[
3 - 2 - 2 - 3 \cdot 2
\][/tex]
6. Multiply [tex]\(3 \cdot 2\)[/tex]:
[tex]\[
3 \cdot 2 = 6
\][/tex]
7. Substitute the result:
[tex]\[
3 - 2 - 2 - 6
\][/tex]
8. Perform the subtractions step by step:
[tex]\[
3 - 2 = 1
\][/tex]
[tex]\[
1 - 2 = -1
\][/tex]
[tex]\[
-1 - 6 = -7
\][/tex]
So, the value of the expression inside the brackets is [tex]\(-7\)[/tex].
Now multiply this result by [tex]\(7 - 5\)[/tex]:
9. Calculate [tex]\(7 - 5\)[/tex]:
[tex]\[
7 - 5 = 2
\][/tex]
10. Finally, multiply the results:
[tex]\[
2 \cdot -7 = -14
\][/tex]
Therefore, the value of the given expression is [tex]\(-14\)[/tex].
[tex]\[
\boxed{-14}
\][/tex]
