https://file.aiquickdraw.com/mathbot/file/1725838056545vb034737.jpg

The problem in the image appears to involve finding the area of a rectangle or surface, described by an algebraic expression.

Here’s a breakdown of the problem and its solution:

### Problem Statement:
You are asked to determine which of the expressions correctly describes the side of a rectangle (or surface) whose area is given by:

\[
28x^2y + 7x^2y - 7xy
\]

We are told that one side of this surface is represented by \( 7xy \). The task is to find the expression for the other side.

### Step-by-Step Solution:
1. **Given Area:** 
   The area of the surface is:
   \[
   28x^2y + 7x^2y - 7xy
   \]

2. **Factor the Area Expression:**
   First, combine like terms:
   \[
   (28x^2y + 7x^2y - 7xy) = 35x^2y - 7xy
   \]

   Now, factor out the greatest common factor (GCF), which is \( 7xy \):
   \[
   35x^2y - 7xy = 7xy(5x - 1)
   \]

3. **Identify the Other Side:**
   Since one side is given as \( 7xy \), the other side is the expression left inside the parentheses after factoring:
   \[
   5x - 1
   \]

Thus, the correct expression for the other side of the rectangle is \( 5x - 1 \).

### Answer:
The correct option is:
\[
\boxed{c) 5x - 1}
\]

---

Do you want more details or have any questions?  
Here are 5 related questions for further exploration:

1. How do you factor expressions with multiple variables?
2. What is the importance of the greatest common factor (GCF) in simplifying expressions?
3. Can you explain how to verify that the factorization is correct by multiplying the factors?
4. What would happen if the expression given was a cubic equation instead of a quadratic?
5. How can factoring help in solving real-world geometric problems like this one?

**Tip:** Always check for common factors before performing any complex operations; it simplifies the problem significantly.

Un rectángulo tiene un área de la superficie de apoyo dada por la expresión 28x^2y + 7x^2y - 7xy. Si uno de los lados de la superficie de apoyo está dado por 7xy, el otro lado está dado por:

Learn how to factor the expression 28x^2y + 7x^2y - 7xy to find the dimensions of a rectangle. This problem involves key algebraic concepts such as factoring and using the greatest common factor (GCF). Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation