Question
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Answer
The simplified form of \( 3dn + 4nd + 7dn \) is \( 14dn \).
Solution
To simplify the expression \( 3dn + 4nd + 7dn \), follow these steps:
1. **Recognize Variable Commutativity:**
- In multiplication, the order of variables doesn't affect the product. Therefore, \( dn = nd \).
2. **Combine Like Terms:**
- \( 3dn + 4nd + 7dn = 3dn + 4dn + 7dn \)
3. **Add the Coefficients:**
- \( 3 + 4 + 7 = 14 \)
4. **Write the Simplified Expression:**
- \( 14dn \)
**Final Simplified Form:**
\[ 14\,d\,n \]
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Simplify this solution Beyond the Answer
To fully simplify the expression \( 3 d n + 4 n d + 7 d n \), we start by noticing that each term has common factors. 1. Rearranging the terms gives us: \( 3 d n + 7 d n + 4 n d \). 2. Since the order of multiplication doesn't matter (commutative property), we can group them by their common factors: \[ (3 + 7 + 4) d n. \] 3. Now, we sum the coefficients: \[ 3 + 7 + 4 = 14. \] Putting it all together, the expression simplifies to: \[ 14 d n. \]
