To evaluate the expression [tex]\((-2+1)^2 + 5 \cdot (12 \div 3) - 9\)[/tex], we will use the order of operations often referred to as PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
1. First, we handle the expression inside the parentheses:
[tex]\[
-2 + 1 = -1
\][/tex]
So, the expression now becomes:
[tex]\[
(-1)^2 + 5 \cdot (12 \div 3) - 9
\][/tex]
2. Next, we take care of the exponentiation:
[tex]\[
(-1)^2 = 1
\][/tex]
Now, the expression is:
[tex]\[
1 + 5 \cdot (12 \div 3) - 9
\][/tex]
3. We then perform the division inside the parentheses:
[tex]\[
12 \div 3 = 4
\][/tex]
Our expression is simplified to:
[tex]\[
1 + 5 \cdot 4 - 9
\][/tex]
4. Now, we proceed with the multiplication:
[tex]\[
5 \cdot 4 = 20
\][/tex]
The expression now reads:
[tex]\[
1 + 20 - 9
\][/tex]
5. Finally, we perform the addition and subtraction from left to right:
[tex]\[
1 + 20 = 21
\][/tex]
[tex]\[
21 - 9 = 12
\][/tex]
Therefore, the value of the expression is [tex]\(12\)[/tex].
