Question

use the order of operations to evaluate this expression:

\\((-2 + 1)^2 + 5(12 \div 3) - 9\\).

type the correct answer in the box. use numerals instead of words.

the value of the expression is .

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Order of Operations",
"PEMDAS"
],
"new_concepts": [],
"current_concepts": [
"Order of Operations",
"PEMDAS"
]
}
</pre_analysis>

<reasoning>

Evaluate operations inside parentheses

\[

$$\begin{aligned} (-2 + 1) &= -1 \\ (12 \div 3) &= 4 \end{aligned}$$

\]

Evaluate exponents and multiplication

\[

$$\begin{aligned} (-1)^2 &= 1 \\ 5(4) &= 20 \end{aligned}$$

\]

Perform addition and subtraction from left to right

\[
1 + 20 - 9 = 21 - 9 = 12
\]
</reasoning>

<answer>
Use the order of operations to evaluate this expression:
\[(-2 + 1)^2 + 5(12 \div 3) - 9\]
Type the correct answer in the box. Use numerals instead of words.

The value of the expression is <blank>12</blank>.
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Order of Operations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Order of Operations",
"PEMDAS"
],
"new_concepts": [],
"current_concepts": [
"Order of Operations",
"PEMDAS"
]
}
</pre_analysis>

<reasoning>

Evaluate operations inside parentheses

\[

$$\begin{aligned} (-2 + 1) &= -1 \\ (12 \div 3) &= 4 \end{aligned}$$

\]

Evaluate exponents and multiplication

\[

$$\begin{aligned} (-1)^2 &= 1 \\ 5(4) &= 20 \end{aligned}$$

\]

Perform addition and subtraction from left to right

\[
1 + 20 - 9 = 21 - 9 = 12
\]
</reasoning>

<answer>
Use the order of operations to evaluate this expression:
\[(-2 + 1)^2 + 5(12 \div 3) - 9\]
Type the correct answer in the box. Use numerals instead of words.

The value of the expression is <blank>12</blank>.
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Order of Operations"
]
}
</post_analysis>