Answer :
To evaluate the expression \( 6 \cdot (4 + 2)^2 - 3^2 \), we will solve it step by step, respecting the order of operations (parentheses, exponents, multiplication and division, and addition and subtraction — PEMDAS).
1. Evaluate the expression inside the parentheses first:
[tex]\[ 4 + 2 = 6 \][/tex]
2. Next, handle the exponentiation within the expression:
[tex]\[ (4 + 2)^2 = 6^2 = 36 \][/tex]
3. Now, multiply 6 by the result of the square:
[tex]\[ 6 \cdot 36 = 216 \][/tex]
4. Evaluate the other exponentiation:
[tex]\[ 3^2 = 9 \][/tex]
5. Finally, subtract the result of \( 3^2 \) from the result of \( 6 \cdot 36 \):
[tex]\[ 216 - 9 = 207 \][/tex]
The final result is \( 207 \).
Thus, the correct answer is [tex]\( \boxed{207} \)[/tex].
1. Evaluate the expression inside the parentheses first:
[tex]\[ 4 + 2 = 6 \][/tex]
2. Next, handle the exponentiation within the expression:
[tex]\[ (4 + 2)^2 = 6^2 = 36 \][/tex]
3. Now, multiply 6 by the result of the square:
[tex]\[ 6 \cdot 36 = 216 \][/tex]
4. Evaluate the other exponentiation:
[tex]\[ 3^2 = 9 \][/tex]
5. Finally, subtract the result of \( 3^2 \) from the result of \( 6 \cdot 36 \):
[tex]\[ 216 - 9 = 207 \][/tex]
The final result is \( 207 \).
Thus, the correct answer is [tex]\( \boxed{207} \)[/tex].
