Pregunta
Find the sum and choose the correct answer. \( 2 n^{3}+4 n^{2}-7 \) and \( -n^{3}+8 n-9 \) \( n^{3}+4 n^{2}+8 n-16 \) \( 3 n^{3}+4 n^{2}+8 n-2 \) \( -n^{3}-4 n^{2}-8 n-16 \) \( n^{3}+4 n^{2}+8 n+16 \)
Ask by Ryan Bates. in the United States
Feb 27,2025
Solución de inteligencia artificial de Upstudy
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The sum is \( n^{3} + 4n^{2} + 8n - 16 \).
Solución
To find the sum, add the like terms from each polynomial:
1. For n³: 2n³ + (–n³) = n³
2. For n²: 4n² (only from the first polynomial)
3. For n: 0 + 8n = 8n
4. For the constant: –7 + (–9) = –16
Thus, the sum is: n³ + 4n² + 8n – 16
The correct answer is: n³ + 4n² + 8n – 16.
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Simplifique esta solución Bonus Knowledge
Let's combine the expressions step by step! First, we'll add \( 2n^{3} + 4n^{2} - 7 \) and \( -n^{3} + 8n - 9 \): 1. Combine the \( n^{3} \) terms: \( 2n^{3} - n^{3} = n^{3} \) 2. Combine the \( n^{2} \) terms: \( 4n^{2} + 0 = 4n^{2} \) 3. Combine the \( n \) terms: \( 0 + 8n = 8n \) 4. Combine the constant terms: \( -7 - 9 = -16 \) Putting it all together gives us: \[ n^{3} + 4n^{2} + 8n - 16 \] So the correct answer is: \( n^{3}+4 n^{2}+8 n-16 \)
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