Question
Perform the operation. (Simplify your answer completely.) \[ \begin{array}{r}5 m^{5}+m^{3}+6 m^{2}-m \\ -\left(6 m^{5}-4 m^{3}+m^{2}+m\right)\end{array} \] SUBMIT ANSWER
Ask by Harrington Fitzgerald. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
- m^{5} + 5 m^{3} + 5 m^{2} - 2 m
\]
Solution
To perform the operation and simplify the expression:
\[
\begin{array}{r}
5 m^{5} + m^{3} + 6 m^{2} - m \\
- \left(6 m^{5} - 4 m^{3} + m^{2} + m\right)
\end{array}
\]
**Step 1: Distribute the negative sign**
\[
5 m^{5} + m^{3} + 6 m^{2} - m - 6 m^{5} + 4 m^{3} - m^{2} - m
\]
**Step 2: Combine like terms**
\[
(5 m^{5} - 6 m^{5}) + (m^{3} + 4 m^{3}) + (6 m^{2} - m^{2}) + (-m - m)
\]
**Step 3: Simplify each group**
\[
- m^{5} + 5 m^{3} + 5 m^{2} - 2 m
\]
**Final Simplified Answer:**
\[
- m^{5} + 5 m^{3} + 5 m^{2} - 2 m
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To perform the operation, first distribute the negative sign in the second expression: \[ 5m^{5} + m^{3} + 6m^{2} - m - (6m^{5} - 4m^{3} + m^{2} + m) \] This becomes: \[ 5m^{5} + m^{3} + 6m^{2} - m - 6m^{5} + 4m^{3} - m^{2} - m \] Now, combine like terms: - For \(m^{5}\): \(5m^{5} - 6m^{5} = -1m^{5}\) - For \(m^{3}\): \(1m^{3} + 4m^{3} = 5m^{3}\) - For \(m^{2}\): \(6m^{2} - 1m^{2} = 5m^{2}\) - For \(m\): \(-1m - 1m = -2m\) Putting it all together, we simplify the expression to: \[ -m^{5} + 5m^{3} + 5m^{2} - 2m \] So, the final answer is: \[ -m^{5} + 5m^{3} + 5m^{2} - 2m \]
