Question

what is the completely factored form of \\(8x^2 - 50\\)?

\\(2(x + 5)(x - 5)\\)
\\(2(2x - 5)(2x - 5)\\)
\\(2(2x + 5)(2x + 5)\\)
\\(2(2x + 5)(2x - 5)\\)

Explanation:

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<reasoning>

Factor out the greatest common factor

\[
8x^2 - 50 = 2(4x^2 - 25)
\]

Factor the difference of squares

\[
4x^2 - 25 = (2x)^2 - (5)^2 = (2x + 5)(2x - 5)
\]

Combine the factors

\[
8x^2 - 50 = 2(2x + 5)(2x - 5)
\]
</reasoning>

<answer>
<mcq-option>\(2(x + 5)(x - 5)\)</mcq-option>
<mcq-option>\(2(2x - 5)(2x - 5)\)</mcq-option>
<mcq-option>\(2(2x + 5)(2x + 5)\)</mcq-option>
<mcq-correct>\(2(2x + 5)(2x - 5)\)</mcq-correct>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
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]
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Answer:

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</pre_analysis>

<reasoning>

Factor out the greatest common factor

\[
8x^2 - 50 = 2(4x^2 - 25)
\]

Factor the difference of squares

\[
4x^2 - 25 = (2x)^2 - (5)^2 = (2x + 5)(2x - 5)
\]

Combine the factors

\[
8x^2 - 50 = 2(2x + 5)(2x - 5)
\]
</reasoning>

<answer>
<mcq-option>\(2(x + 5)(x - 5)\)</mcq-option>
<mcq-option>\(2(2x - 5)(2x - 5)\)</mcq-option>
<mcq-option>\(2(2x + 5)(2x + 5)\)</mcq-option>
<mcq-correct>\(2(2x + 5)(2x - 5)\)</mcq-correct>
</answer>

<post_analysis>
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"knowledge_point": [
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]
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