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