Question
Subtract. \( \left(4 m^{3}+6\right)-\left(-2 m^{3}+m^{2}+3\right) \) \( 6 m^{3}+m^{2}+3 \) \( 6 m^{3}+5 m^{2}-3 \) \( 6 m^{3}-m^{2}+3 \) \( 2 m^{3}+m^{2}+9 \)
Ask by Davies Turner. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 6 m^{3} - m^{2} + 3 \)
Solution
Let's perform the subtraction step by step:
Given:
\[
\left(4 m^{3} + 6\right) - \left(-2 m^{3} + m^{2} + 3\right)
\]
1. **Distribute the negative sign:**
\[
4 m^{3} + 6 + 2 m^{3} - m^{2} - 3
\]
2. **Combine like terms:**
- **\( m^{3} \) terms:** \( 4 m^{3} + 2 m^{3} = 6 m^{3} \)
- **\( m^{2} \) terms:** \( -m^{2} \) (only one term)
- **Constant terms:** \( 6 - 3 = 3 \)
3. **Write the simplified expression:**
\[
6 m^{3} - m^{2} + 3
\]
**Therefore, the correct answer is:**
\[
6 m^{3} - m^{2} + 3
\]
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Simplify this solution Bonus Knowledge
Let's break it down step-by-step for clarity! First, distribute the negative sign through the second parentheses: \[ \left(4 m^{3} + 6\right) - \left(-2 m^{3} + m^{2} + 3\right) = 4 m^{3} + 6 + 2 m^{3} - m^{2} - 3 \] Now, combine the like terms: 1. Combine the \(m^{3}\) terms: \(4 m^{3} + 2 m^{3} = 6 m^{3}\) 2. Combine the constant terms: \(6 - 3 = 3\) 3. The \(m^{2}\) term remains as \(-m^{2}\) Putting it all together, we have: \[ 6 m^{3} - m^{2} + 3 \] So, the correct answer is \(6 m^{3} - m^{2} + 3\).
