Question

which equation is true?
\\(9x^2 - 25 = (3x - 5)(3x - 5)\\)
\\(9x^2 - 25 = (3x - 5)(3x + 5)\\)
\\(9x^2 - 25 = -(3x + 5)(3x + 5)\\)
\\(9x^2 - 25 = -(3x + 5)(3x - 5)\\)

Explanation:

<pre_analysis>
{
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"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Difference of Squares"
],
"new_concepts": [],
"current_concepts": [
"Difference of Squares",
"Factoring Polynomials"
]
}
</pre_analysis>

<reasoning>

Identify the algebraic structure

\[
9x^2 - 25 = (3x)^2 - 5^2
\]

Apply the difference of squares formula

\[
a^2 - b^2 = (a - b)(a + b)
\]
\[
(3x)^2 - 5^2 = (3x - 5)(3x + 5)
\]

Match with the given options

\[
9x^2 - 25 = (3x - 5)(3x + 5)
\]
</reasoning>

<answer>
<mcq-option>(A) \(9x^2 - 25 = (3x - 5)(3x - 5)\)</mcq-option>
<mcq-correct>(B) \(9x^2 - 25 = (3x - 5)(3x + 5)\)</mcq-correct>
<mcq-option>(C) \(9x^2 - 25 = -(3x + 5)(3x + 5)\)</mcq-option>
<mcq-option>(D) \(9x^2 - 25 = -(3x + 5)(3x - 5)\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Difference of Squares"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Difference of Squares"
],
"new_concepts": [],
"current_concepts": [
"Difference of Squares",
"Factoring Polynomials"
]
}
</pre_analysis>

<reasoning>

Identify the algebraic structure

\[
9x^2 - 25 = (3x)^2 - 5^2
\]

Apply the difference of squares formula

\[
a^2 - b^2 = (a - b)(a + b)
\]
\[
(3x)^2 - 5^2 = (3x - 5)(3x + 5)
\]

Match with the given options

\[
9x^2 - 25 = (3x - 5)(3x + 5)
\]
</reasoning>

<answer>
<mcq-option>(A) \(9x^2 - 25 = (3x - 5)(3x - 5)\)</mcq-option>
<mcq-correct>(B) \(9x^2 - 25 = (3x - 5)(3x + 5)\)</mcq-correct>
<mcq-option>(C) \(9x^2 - 25 = -(3x + 5)(3x + 5)\)</mcq-option>
<mcq-option>(D) \(9x^2 - 25 = -(3x + 5)(3x - 5)\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Difference of Squares"
]
}
</post_analysis>