Question

simplify: \\((-\sqrt{x-4})^2\\)

\\(\bigcirc\\) \\(-x+4\\)
\\(\bigcirc\\) \\(x-4\\)
\\(\bigcirc\\) \\(2x-8\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Exponent Rules",
"Algebraic Simplification"
],
"new_concepts": [],
"current_concepts": [
"Exponent Rules",
"Algebraic Simplification",
"Radical Expressions"
]
}
</pre_analysis>

<reasoning>

Apply the power of a product rule

Using the Exponent Rules knowledge point
\[
(-\sqrt{x-4})^2 = (-1)^2 \cdot (\sqrt{x-4})^2
\]

Simplify the squared terms

Using the Algebraic Simplification knowledge point
\[

$$\begin{aligned} (-1)^2 &= 1 \\ (\sqrt{x-4})^2 &= x - 4 \quad (\text{for } x \ge 4) \\ (-\sqrt{x-4})^2 &= 1 \cdot (x - 4) = x - 4 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>-x + 4</mcq-option>
<mcq-correct>x - 4</mcq-correct>
<mcq-option>2x - 8</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Radical Expressions"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Exponent Rules",
"Algebraic Simplification"
],
"new_concepts": [],
"current_concepts": [
"Exponent Rules",
"Algebraic Simplification",
"Radical Expressions"
]
}
</pre_analysis>

<reasoning>

Apply the power of a product rule

Using the Exponent Rules knowledge point
\[
(-\sqrt{x-4})^2 = (-1)^2 \cdot (\sqrt{x-4})^2
\]

Simplify the squared terms

Using the Algebraic Simplification knowledge point
\[

$$\begin{aligned} (-1)^2 &= 1 \\ (\sqrt{x-4})^2 &= x - 4 \quad (\text{for } x \ge 4) \\ (-\sqrt{x-4})^2 &= 1 \cdot (x - 4) = x - 4 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>-x + 4</mcq-option>
<mcq-correct>x - 4</mcq-correct>
<mcq-option>2x - 8</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Radical Expressions"
]
}
</post_analysis>