To simplify the expression [tex]\(3 \cdot 3^2 + 8 \div 2 - (4 + 3)\)[/tex], we will 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. Parentheses:
Simplify the expression inside the parentheses:
[tex]\[
(4 + 3) = 7
\][/tex]
2. Exponents:
Calculate the exponent next:
[tex]\[
3^2 = 9
\][/tex]
3. Multiplication:
Perform the multiplication:
[tex]\[
3 \cdot 9 = 27
\][/tex]
4. Division:
Perform the division:
[tex]\[
8 \div 2 = 4
\][/tex]
5. Substitute back into the expression:
Now we have:
[tex]\[
27 + 4 - 7
\][/tex]
6. Addition and Subtraction:
Perform the addition and subtraction from left to right:
[tex]\[
27 + 4 = 31
\][/tex]
[tex]\[
31 - 7 = 24
\][/tex]
So, the simplified value of the expression [tex]\(3 \cdot 3^2 + 8 \div 2 - (4 + 3)\)[/tex] is [tex]\(24\)[/tex].
The correct answer is:
[tex]\[
\boxed{24}
\][/tex]
