To simplify the expression [tex]\(\left(11 - \frac{2}{5} \sqrt{25}\right)^2 + (1 - 4)^2\)[/tex], we will break it down step-by-step:
1. Evaluate the square root:
[tex]\[
\sqrt{25} = 5
\][/tex]
2. Multiply within the expression:
[tex]\[
\frac{2}{5} \cdot 5 = 2
\][/tex]
3. Simplify the expression inside the first parentheses:
[tex]\[
11 - 2 = 9
\][/tex]
4. Square the result from the first parentheses:
[tex]\[
9^2 = 81
\][/tex]
5. Simplify the expression inside the second parentheses:
[tex]\[
1 - 4 = -3
\][/tex]
6. Square the result from the second parentheses:
[tex]\[
(-3)^2 = 9
\][/tex]
7. Add the squared results together:
[tex]\[
81 + 9 = 90
\][/tex]
Thus, the simplified result of the expression [tex]\(\left(11 - \frac{2}{5} \sqrt{25}\right)^2 + (1 - 4)^2\)[/tex] is:
[tex]\[
\boxed{90}
\][/tex]
