Question

reescribe la expresión \\((x + 6)(4x - 3)\\) escribe tu trabajo en tu página \muestra tu trabajo\.

a) \\(4x^2 - 3x + 18\\)
b) \\(4x^2 + 24x - 18\\)
c) \\(4x^2 + 21x - 18\\)
d) \\(4x^2 + 3x - 18\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
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"concepts_used": [
"Polynomial Multiplication"
],
"new_concepts": [],
"current_concepts": [
"Polynomial Multiplication",
"Special Products"
]
}
</pre_analysis>

<reasoning>

Aplicar la propiedad distributiva

\[
(x + 6)(4x - 3) = x(4x - 3) + 6(4x - 3)
\]

Expandir los términos

\[
x(4x - 3) + 6(4x - 3) = 4x^2 - 3x + 24x - 18
\]

Simplificar términos semejantes

\[
4x^2 + (-3x + 24x) - 18 = 4x^2 + 21x - 18
\]
</reasoning>

<answer>
<mcq-option>(A) \(4x^2 - 3x + 18\)</mcq-option>
<mcq-option>(B) \(4x^2 + 24x - 18\)</mcq-option>
<mcq-correct>(C) \(4x^2 + 21x - 18\)</mcq-correct>
<mcq-option>(D) \(4x^2 + 3x - 18\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Polynomial Multiplication"
]
}
</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": [
"Polynomial Multiplication"
],
"new_concepts": [],
"current_concepts": [
"Polynomial Multiplication",
"Special Products"
]
}
</pre_analysis>

<reasoning>

Aplicar la propiedad distributiva

\[
(x + 6)(4x - 3) = x(4x - 3) + 6(4x - 3)
\]

Expandir los términos

\[
x(4x - 3) + 6(4x - 3) = 4x^2 - 3x + 24x - 18
\]

Simplificar términos semejantes

\[
4x^2 + (-3x + 24x) - 18 = 4x^2 + 21x - 18
\]
</reasoning>

<answer>
<mcq-option>(A) \(4x^2 - 3x + 18\)</mcq-option>
<mcq-option>(B) \(4x^2 + 24x - 18\)</mcq-option>
<mcq-correct>(C) \(4x^2 + 21x - 18\)</mcq-correct>
<mcq-option>(D) \(4x^2 + 3x - 18\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Polynomial Multiplication"
]
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</post_analysis>