Pregunta
3. Write down the constant term: a) \( 7 x-3 y+2 \) c) \( 5 r-4 y-4-2 x \) e) \( 5+2(6 x-4 y) \)
Ask by Mathis Nichols. in South Africa
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
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- **a)** 2
- **c)** -4
- **e)** 5
Solución
Certainly! Let's identify the **constant term** in each of the given expressions. The constant term is the term that does not contain any variables.
### a) \( 7x - 3y + 2 \)
- **Terms:**
- \( 7x \) (variable term)
- \( -3y \) (variable term)
- \( +2 \) (**constant term**)
- **Constant Term:** **2**
---
### c) \( 5r - 4y - 4 - 2x \)
- **Terms:**
- \( 5r \) (variable term)
- \( -4y \) (variable term)
- \( -4 \) (**constant term**)
- \( -2x \) (variable term)
- **Constant Term:** **-4**
---
### e) \( 5 + 2(6x - 4y) \)
First, let's simplify the expression:
\[
5 + 2(6x - 4y) = 5 + 12x - 8y
\]
- **Terms after simplification:**
- \( 12x \) (variable term)
- \( -8y \) (variable term)
- \( +5 \) (**constant term**)
- **Constant Term:** **5**
---
### **Summary of Constant Terms:**
- **a)** 2
- **c)** -4
- **e)** 5
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The Deep Dive
In the expression \( 7 x - 3 y + 2 \), the constant term is simply the number without any variables, which is \( 2 \). For the expression \( 5r - 4y - 4 - 2x \), the constant term is \( -4 \), as it’s the only term without a variable attached to it. In the expression \( 5 + 2(6x - 4y) \), you first need to simplify: \( 5 + 12x - 8y \). Here, the constant term is \( 5 \).
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