To solve the expression [tex]\(3 \cdot (5 + 4)^2 - 4^2\)[/tex], let's break it down step by step:
1. Calculate the sum inside the parentheses:
[tex]\[
5 + 4 = 9
\][/tex]
2. Square the result of the sum inside the parentheses:
[tex]\[
9^2 = 81
\][/tex]
3. Multiply the squared result by 3:
[tex]\[
3 \cdot 81 = 243
\][/tex]
4. Square 4:
[tex]\[
4^2 = 16
\][/tex]
5. Subtract the squared value of 4 from the product obtained in step 3:
[tex]\[
243 - 16 = 227
\][/tex]
Hence, the value of the expression [tex]\(3 \cdot (5 + 4)^2 - 4^2\)[/tex] is 227.
Therefore, the correct answer is:
[tex]\[
\boxed{B \, 227}
\][/tex]
