Question

question 10

subtract the following polynomials: \\((15n + 5n^7 + 14n^4) - (-2n^4 + 3n^7 + 2n)\\)

\\(2n^7 + 16n^4 + 13n\\)
\\(31n^{13}\\)
\\(2n^7 + 12n^4 + 13n\\)
\\(8n^7 + 12n^4 + 17n\\)

Explanation:

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<reasoning>

Distribute the negative sign

\[
(15n + 5n^7 + 14n^4) - (-2n^4 + 3n^7 + 2n) = 15n + 5n^7 + 14n^4 + 2n^4 - 3n^7 - 2n
\]

Group and combine like terms

\[

$$\begin{aligned} (5n^7 - 3n^7) + (14n^4 + 2n^4) + (15n - 2n) &= (5 - 3)n^7 + (14 + 2)n^4 + (15 - 2)n\\ &= 2n^7 + 16n^4 + 13n \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(2n^7 + 16n^4 + 13n\)</mcq-correct>
<mcq-option>(B) \(31n^{13}\)</mcq-option>
<mcq-option>(C) \(2n^7 + 12n^4 + 13n\)</mcq-option>
<mcq-option>(D) \(8n^7 + 12n^4 + 17n\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Distribute the negative sign

\[
(15n + 5n^7 + 14n^4) - (-2n^4 + 3n^7 + 2n) = 15n + 5n^7 + 14n^4 + 2n^4 - 3n^7 - 2n
\]

Group and combine like terms

\[

$$\begin{aligned} (5n^7 - 3n^7) + (14n^4 + 2n^4) + (15n - 2n) &= (5 - 3)n^7 + (14 + 2)n^4 + (15 - 2)n\\ &= 2n^7 + 16n^4 + 13n \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(2n^7 + 16n^4 + 13n\)</mcq-correct>
<mcq-option>(B) \(31n^{13}\)</mcq-option>
<mcq-option>(C) \(2n^7 + 12n^4 + 13n\)</mcq-option>
<mcq-option>(D) \(8n^7 + 12n^4 + 17n\)</mcq-option>
</answer>

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