Let's evaluate the expression step-by-step:
[tex]\[
3 \cdot (5 + 4)^2 - 4^2
\][/tex]
1. First, calculate inside the parentheses:
[tex]\[
5 + 4 = 9
\][/tex]
2. Next, raise the result to the power of 2:
[tex]\[
9^2 = 81
\][/tex]
3. Now, multiply by 3:
[tex]\[
3 \cdot 81 = 243
\][/tex]
4. Compute the square of 4:
[tex]\[
4^2 = 16
\][/tex]
5. Finally, subtract the result of the second square from the first multiplication:
[tex]\[
243 - 16 = 227
\][/tex]
Thus, the value of the expression is:
[tex]\[
227
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{A}
\][/tex]
