Question
Identify the coefficients in the following expression. \[ \pi u v+4 u+6 v+3 \]
Ask by Li Mccarthy. in Canada
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The coefficients in the expression are:
- \(\pi\) for \(uv\)
- \(4\) for \(u\)
- \(6\) for \(v\)
- \(3\) as the constant term
Solution
To identify the coefficients in the expression
\[
\pi u v + 4 u + 6 v + 3,
\]
we can break it down term by term:
1. **Term**: \(\pi u v\)
- Coefficient: \(\pi\) (the coefficient of the product \(uv\))
2. **Term**: \(4 u\)
- Coefficient: \(4\) (the coefficient of \(u\))
3. **Term**: \(6 v\)
- Coefficient: \(6\) (the coefficient of \(v\))
4. **Term**: \(3\)
- Coefficient: \(3\) (this is the constant term, which can be considered as the coefficient of \(1\))
In summary, the coefficients in the expression are:
- Coefficient of \(uv\): \(\pi\)
- Coefficient of \(u\): \(4\)
- Coefficient of \(v\): \(6\)
- Constant term: \(3\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
In the expression \(\pi u v + 4u + 6v + 3\), the coefficients can be identified as follows: For the term \(\pi u v\), the coefficient is \(\pi\), though it is technically more complex as it involves two variables. For the linear terms, the coefficient of \(u\) is \(4\), the coefficient of \(v\) is \(6\), and the constant term is \(3\). So, to sum it up, the coefficients are \(\pi\), \(4\), \(6\), and \(3\).
