To evaluate the expression
[tex]\[
6 \cdot (4+2)^2 - 3^2
\][/tex]
we will follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
1. Parentheses: Evaluate the expression inside the parentheses first:
[tex]\[
4 + 2 = 6
\][/tex]
2. Exponents: Next, evaluate the exponentiation:
[tex]\[
(6)^2 = 36
\][/tex]
and separately:
[tex]\[
3^2 = 9
\][/tex]
3. Multiplication: Now, multiply:
[tex]\[
6 \cdot 36 = 216
\][/tex]
4. Subtraction: Finally, subtract the results of the exponentiations:
[tex]\[
216 - 9 = 207
\][/tex]
Therefore, the value of the expression
[tex]\[
6 \cdot(4+2)^2 - 3^2
\][/tex]
is
[tex]\[
\boxed{207}
\][/tex]
