Certainly! Let's analyze the given algebraic expression step-by-step:
The expression is:
\(\[ xy + 5y + 2x \]\)
### Step 1: Identify the Terms
The given expression has three terms:
1. \(\( xy \)\)
2. \(\( 5y \)\)
3. \(\( 2x \)\)
### Step 2: Observation of Terms
Upon analyzing these terms, you will notice that:
- The first term, \(\( xy \)\), is a product of two variables \(\( x \)\) and \(\( y \)\).
- The second term, \(\( 5y \)\), is a product of the variable \(\( y \)\) and a constant \(\( 5 \)\).
- The third term, \(\( 2x \)\), is a product of the variable \(\( x \)\) and a constant \(\( 2 \)\).
### Step 3: Group the Terms
We are instructed to group the first two terms and then the last term. So, we will group as follows:
\(\[ (xy + 5y) + 2x \]\)
### Step 4: Factor Each Group
Now, let's factor each group separately:
1. Group 1: \(\( xy + 5y \)\)
- We can factor out the common variable \(\( y \)\) from the terms \(\( xy \)\) and \(\( 5y \)\):
\(\[ y(x + 5) \]\)
2. Group 2: \(\( 2x \)\)
- This term is already fully factored as \(\( 2x \)\).
### Step 5: Combine the Factored Results
Finally, we add the factored results of Group 1 and Group 2:
\(\[ y(x + 5) + 2x \]\)
### Summary
So, the original expression \(\( xy + 5y + 2x \)\) after grouping and factoring becomes:
\(\[ y(x + 5) + 2x \]\)
This process simplifies the expression and can help in understanding the structure of the polynomial better as well as being useful for further algebraic manipulations.
