Sure, let's solve the expression step-by-step.
### Given Expression:
[tex]\[ 2 \cdot (6-2)^2 - (7 \cdot 2 + 1) / 3 \][/tex]
1. Evaluate the expression inside the parentheses:
[tex]\[
6 - 2 = 4
\][/tex]
2. Square the result of the inner parentheses:
[tex]\[
4^2 = 16
\][/tex]
3. Multiply the squared value by 2:
[tex]\[
2 \cdot 16 = 32
\][/tex]
4. Evaluate the expression inside the second set of parentheses:
[tex]\[
7 \cdot 2 + 1 = 14 + 1 = 15
\][/tex]
5. Divide the result by 3:
[tex]\[
15 / 3 = 5.0
\][/tex]
6. Subtract the divided value from the multiplied value:
[tex]\[
32 - 5.0 = 27.0
\][/tex]
Thus, the value of the expression [tex]\( 2 \cdot (6-2)^2 - (7 \cdot 2 + 1) / 3 \)[/tex] is:
[tex]\[
\boxed{27.0}
\][/tex]
