Question

find: \\((4x^2y^3 + 2xy^2 - 2y) - (-7x^2y^3 + 6xy^2 - 2y)\\)

place the correct coefficients in the difference.

\\(\quadx^2y^3 + \quadxy^2 + \quady\\)

Explanation:

<pre_analysis>
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"Like Terms",
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<reasoning>

Distribute the negative sign

\[
(4x^2y^3 + 2xy^2 - 2y) - (-7x^2y^3 + 6xy^2 - 2y) = 4x^2y^3 + 2xy^2 - 2y + 7x^2y^3 - 6xy^2 + 2y
\]

Group and combine like terms

\[

$$\begin{aligned} &(4 + 7)x^2y^3 + (2 - 6)xy^2 + (-2 + 2)y \\ &= 11x^2y^3 - 4xy^2 + 0y \end{aligned}$$

\]
</reasoning>

<answer>
Find: \((4x^2y^3 + 2xy^2 - 2y) - (-7x^2y^3 + 6xy^2 - 2y)\)

Place the correct coefficients in the difference.
<blank>11</blank>\(x^2y^3 +\) <blank>-4</blank>\(xy^2 +\) <blank>0</blank>\(y\)
</answer>

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

Answer:

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"step_cot",
"blank_filling_formatter",
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"Polynomial Subtraction",
"Like Terms",
"Additive Inverse"
],
"new_concepts": [],
"current_concepts": [
"Polynomial Subtraction",
"Like Terms",
"Additive Inverse"
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</pre_analysis>

<reasoning>

Distribute the negative sign

\[
(4x^2y^3 + 2xy^2 - 2y) - (-7x^2y^3 + 6xy^2 - 2y) = 4x^2y^3 + 2xy^2 - 2y + 7x^2y^3 - 6xy^2 + 2y
\]

Group and combine like terms

\[

$$\begin{aligned} &(4 + 7)x^2y^3 + (2 - 6)xy^2 + (-2 + 2)y \\ &= 11x^2y^3 - 4xy^2 + 0y \end{aligned}$$

\]
</reasoning>

<answer>
Find: \((4x^2y^3 + 2xy^2 - 2y) - (-7x^2y^3 + 6xy^2 - 2y)\)

Place the correct coefficients in the difference.
<blank>11</blank>\(x^2y^3 +\) <blank>-4</blank>\(xy^2 +\) <blank>0</blank>\(y\)
</answer>

<post_analysis>
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"Mathematics",
"Algebra",
"Polynomial Subtraction"
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</post_analysis>