Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 12k^{3} + 5k^{2} + 9k \)
Solution
To simplify the expression \( 8k^{2} + 5k^{3} - 3k^{2} + 9k + 7k^{3} \), follow these steps:
1. **Combine like terms:**
- **\( k^{3} \) terms:**
\[
5k^{3} + 7k^{3} = 12k^{3}
\]
- **\( k^{2} \) terms:**
\[
8k^{2} - 3k^{2} = 5k^{2}
\]
- **\( k \) terms:**
\[
9k \quad (\text{only one term})
\]
2. **Write the simplified expression:**
\[
12k^{3} + 5k^{2} + 9k
\]
This is the fully simplified form of the given polynomial.
**Final Answer:**
\[
12k^{3} + 5k^{2} + 9k
\]
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Simplify this solution Bonus Knowledge
To simplify the expression \( 8 k^{2} + 5 k^{3} - 3 k^{2} + 9 k + 7 k^{3} \), we start by combining like terms. 1. First, group the \( k^{3} \) terms together: \[ 5 k^{3} + 7 k^{3} = 12 k^{3} \] 2. Next, combine the \( k^{2} \) terms: \[ 8 k^{2} - 3 k^{2} = 5 k^{2} \] 3. Finally, include the \( k \) term: \[ + 9 k \] Now, putting it all together, we have: \[ 12 k^{3} + 5 k^{2} + 9 k \] Thus, the fully simplified expression is: \[ \boxed{12 k^{3} + 5 k^{2} + 9 k} \]
