Question

find the difference.

\\((x^2 - 4x - 2) - (2x^2 + 2x - 3)\\)

\\(?x^2 + \box x + \box\\)

Explanation:

<pre_analysis>
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"Algebraic Simplification"
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"Distributive Property",
"Algebraic Simplification",
"Polynomial Subtraction",
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</pre_analysis>

<reasoning>

Distribute the negative sign

Using the Distributive Property knowledge point
\[
-(2x^2 + 2x - 3) = -2x^2 - 2x + 3
\]

Rewrite the entire expression

Using the Algebraic Simplification knowledge point
\[
(x^2 - 4x - 2) - (2x^2 + 2x - 3) = x^2 - 4x - 2 - 2x^2 - 2x + 3
\]

Group and combine like terms

Using the Algebraic Simplification knowledge point
\[

$$\begin{aligned} (x^2 - 2x^2) + (-4x - 2x) + (-2 + 3) &= (1 - 2)x^2 + (-4 - 2)x + 1 \\ &= -1x^2 + (-6)x + 1 \\ &= -x^2 - 6x + 1 \end{aligned}$$

\]
</reasoning>

<answer>
Find the difference.

\[(x^2 - 4x - 2) - (2x^2 + 2x - 3)\]

<blank>\(-1\)</blank>\(x^2 +\) <blank>\(-6\)</blank>\(x +\) <blank>\(1\)</blank>
</answer>

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

Answer:

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"blank_filling_formatter",
"explain_then_answer",
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],
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"Distributive Property",
"Algebraic Simplification",
"Polynomial Subtraction",
"Combining Like Terms"
]
}
</pre_analysis>

<reasoning>

Distribute the negative sign

Using the Distributive Property knowledge point
\[
-(2x^2 + 2x - 3) = -2x^2 - 2x + 3
\]

Rewrite the entire expression

Using the Algebraic Simplification knowledge point
\[
(x^2 - 4x - 2) - (2x^2 + 2x - 3) = x^2 - 4x - 2 - 2x^2 - 2x + 3
\]

Group and combine like terms

Using the Algebraic Simplification knowledge point
\[

$$\begin{aligned} (x^2 - 2x^2) + (-4x - 2x) + (-2 + 3) &= (1 - 2)x^2 + (-4 - 2)x + 1 \\ &= -1x^2 + (-6)x + 1 \\ &= -x^2 - 6x + 1 \end{aligned}$$

\]
</reasoning>

<answer>
Find the difference.

\[(x^2 - 4x - 2) - (2x^2 + 2x - 3)\]

<blank>\(-1\)</blank>\(x^2 +\) <blank>\(-6\)</blank>\(x +\) <blank>\(1\)</blank>
</answer>

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