Question
Combine: \( \left(3 n^{3}+7 n-2\right)+\left(12 n^{3}-3 n+9\right) \)
Ask by Hill Hall. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Combine like terms to get \(15n^{3} + 4n + 7\).
Solution
To combine the expressions \( \left(3n^{3} + 7n - 2\right) + \left(12n^{3} - 3n + 9\right) \), follow these steps:
1. **Remove the parentheses:**
\[
3n^{3} + 7n - 2 + 12n^{3} - 3n + 9
\]
2. **Combine like terms:**
- **Cubic terms (\(n^3\)):**
\[
3n^{3} + 12n^{3} = 15n^{3}
\]
- **Linear terms (\(n\)):**
\[
7n - 3n = 4n
\]
- **Constant terms:**
\[
-2 + 9 = 7
\]
3. **Write the simplified expression:**
\[
15n^{3} + 4n + 7
\]
**Final Answer:**
\[
15n^{3} + 4n + 7
\]
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Simplify this solution Bonus Knowledge
To combine the expressions \( (3n^{3} + 7n - 2) + (12n^{3} - 3n + 9) \), start by grouping like terms together: 1. Combine the \( n^{3} \) terms: \( 3n^{3} + 12n^{3} = 15n^{3} \) 2. Combine the \( n \) terms: \( 7n - 3n = 4n \) 3. Combine the constant terms: \( -2 + 9 = 7 \) Putting it all together, the combined expression is: \[ 15n^{3} + 4n + 7 \]
