To simplify the expression [tex]\(6^2 - 3 \cdot 2^2\)[/tex], we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
1. Evaluate the exponents first:
- Calculate [tex]\(6^2\)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
- Calculate [tex]\(2^2\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
2. Next, perform the multiplication:
- Multiply 3 by the result of [tex]\(2^2\)[/tex]:
[tex]\[
3 \cdot 4 = 12
\][/tex]
3. Lastly, perform the subtraction:
- Subtract the result of the multiplication from the result of [tex]\(6^2\)[/tex]:
[tex]\[
36 - 12 = 24
\][/tex]
Therefore, the simplified result of the expression [tex]\(6^2 - 3 \cdot 2^2\)[/tex] is:
[tex]\[
\boxed{24}
\][/tex]
