To evaluate the expression [tex]\((-2 + 1)^2 + 5 \left( \frac{12}{3} \right) - 9\)[/tex] step-by-step, we will follow the order of operations (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right), often abbreviated as PEMDAS.
1. Parentheses:
Begin by evaluating the expression inside the innermost parentheses:
[tex]\[
-2 + 1 = -1
\][/tex]
So, the expression now becomes:
[tex]\[
(-1)^2 + 5 \left( \frac{12}{3} \right) - 9
\][/tex]
2. Exponents:
Next, calculate the exponent:
[tex]\[
(-1)^2 = 1
\][/tex]
So, the expression now is:
[tex]\[
1 + 5 \left( \frac{12}{3} \right) - 9
\][/tex]
3. Division:
Now, perform the division:
[tex]\[
\frac{12}{3} = 4
\][/tex]
So, the expression simplifies to:
[tex]\[
1 + 5 \cdot 4 - 9
\][/tex]
4. Multiplication:
Then, carry out the multiplication:
[tex]\[
5 \cdot 4 = 20
\][/tex]
So the expression becomes:
[tex]\[
1 + 20 - 9
\][/tex]
5. Addition and Subtraction:
Finally, 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].
