Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 5fn + 17f + 6nw \)
Solution
To simplify the expression \( 2fn + 8f + 6nw + 3nf + 9f \), follow these steps:
1. **Combine like terms**:
- **Terms involving \( fn \)**:
\[
2fn + 3nf = 5fn
\]
- **Constant terms involving \( f \)**:
\[
8f + 9f = 17f
\]
- **Term involving \( nw \)**:
\[
6nw \quad (\text{no like terms to combine})
\]
2. **Rewrite the expression with combined terms**:
\[
5fn + 17f + 6nw
\]
3. **Optional: Factor out common variables**:
- You can factor out \( f \) from the first two terms:
\[
f(5n + 17) + 6nw
\]
However, the fully simplified form with like terms combined is:
\[
\boxed{5fn + 17f + 6nw}
\]
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Simplify this solution The Deep Dive
To simplify the expression \( 2fn + 8f + 6nw + 3nf + 9f \), we start by combining like terms: 1. First, identify the terms involving \( f \) and \( n \): - The terms involving \( f \) are \( 8f \) and \( 9f \), as well as \( 2fn \) and \( 3nf \) which can be combined since \( fn \) is the same as \( nf \). - The term involving \( nw \) is \( 6nw \) which doesn't combine with others. 2. Now combine the like terms: - For \( f \): \[ 8f + 9f = 17f \] - For \( nf \): \[ 2fn + 3nf = 5fn \] 3. Substitute these combined terms back into the expression: \[ 5fn + 6nw + 17f \] The fully simplified expression is: \[ 5fn + 6nw + 17f \]
