Construct a table to find the missing term in the product (−9m6+12m5)(m2+2m+1)=−9m8−6m7+?+12m5 .(1 point) Responses 33m6 33 m superscript 6 baseline −9m6 negConstruct a table to find the missing term in the product (−9m6+12m5)(m2+2m+1)=−9m8−6m7+?+12m5 .(1 point) Responses 33m6 33 m superscript 6 baseline −9m6 negative 9 m superscript 6 baseline 3m6 3 m superscript 6 baseline 15m6ative 9 m superscript 6 baseline 3m6 3 m superscript 6 baseline 15m6

Answer 1

To find the missing term in the product \((−9m^6+12m^5)(m^2+2m+1)\), we can perform the polynomial multiplication and look for the missing coefficient associated with \(m^6\).

Let's break it down step-by-step:

1. Distribute \(-9m^6\):

   • \(-9m^6 \cdot m^2 = -9m^8\)
   • \(-9m^6 \cdot 2m = -18m^7\)
   • \(-9m^6 \cdot 1 = -9m^6\)

2. Distribute \(12m^5\):

   • \(12m^5 \cdot m^2 = 12m^7\)
   • \(12m^5 \cdot 2m = 24m^6\)
   • \(12m^5 \cdot 1 = 12m^5\)

3. Combine all the terms:

   • From the distribution, we get:
     • Constant term: \(12m^5\)
     • \(m^6\) terms: \(-9m^6 + 24m^6 = 15m^6\)
     • \(m^7\) terms: \(-18m^7 + 12m^7 = -6m^7\)
     • \(m^8\) term: \(-9m^8\)

4. Putting it all together: \[ (−9m^6+12m^5)(m^2+2m+1) = -9m^8 - 6m^7 + 15m^6 + 12m^5 \]

Thus, the missing term is 15m^6.

Final answer:

Response: 15m^6

Answer 2

Hope its right

Answer 3

Yes, based on the calculations, the answer is correct! The missing term in the product \((−9m^6+12m^5)(m^2+2m+1)\) is indeed \(15m^6\).

To recap briefly:

1. We distributed both \(-9m^6\) and \(12m^5\) across \(m^2 + 2m + 1\).
2. We collected like terms for \(m^8\), \(m^7\), \(m^6\), and the constant term.
3. The correct coefficient for \(m^6\) in the final expression was found to be \(15\).

If you have any further questions or need clarifications, feel free to ask!