In each polynomial, given below, separate the like terms :
`y^(2)z^(3), xy^(2)z^(3), -5x^(2)yz, -4y^(2)z^(3), -8xz^(3)y^(2), 3x^(2)yz` and `2z^(3)y^(2)`

Answer

To separate the like terms in the given polynomial expressions, we will follow these steps:

### Step 1: Identify the Terms
The given polynomial terms are:
1. \( y^2 z^3 \)
2. \( xy^2 z^3 \)
3. \( -5x^2 yz \)
4. \( -4y^2 z^3 \)
5. \( -8xz^3y^2 \)
6. \( 3x^2 yz \)
7. \( 2z^3y^2 \)

### Step 2: Group the Like Terms
Like terms are terms that have the same variables raised to the same powers. We will group them based on their variable composition.

#### Group 1: Terms with \( y^2 z^3 \)
- \( y^2 z^3 \)
- \( -4y^2 z^3 \)
- \( 2z^3y^2 \)

These terms can be grouped together because they all contain \( y^2 \) and \( z^3 \).

#### Group 2: Terms with \( xy^2 z^3 \)
- \( xy^2 z^3 \)
- \( -8xz^3y^2 \)

These terms can be grouped together because they both contain \( x \), \( y^2 \), and \( z^3 \).

#### Group 3: Terms with \( x^2 yz \)
- \( -5x^2 yz \)
- \( 3x^2 yz \)

These terms can be grouped together because they both contain \( x^2 \), \( y \), and \( z \).

### Step 3: Write the Grouped Like Terms
Now we can write the like terms together:
1. For \( y^2 z^3 \): \( y^2 z^3, -4y^2 z^3, 2z^3y^2 \)
2. For \( xy^2 z^3 \): \( xy^2 z^3, -8xz^3y^2 \)
3. For \( x^2 yz \): \( -5x^2 yz, 3x^2 yz \)

### Final Grouping of Like Terms
- **Group 1**: \( y^2 z^3, -4y^2 z^3, 2z^3y^2 \)
- **Group 2**: \( xy^2 z^3, -8xz^3y^2 \)
- **Group 3**: \( -5x^2 yz, 3x^2 yz \)

### Summary of Like Terms
1. \( y^2 z^3, -4y^2 z^3, 2z^3y^2 \)
2. \( xy^2 z^3, -8xz^3y^2 \)
3. \( -5x^2 yz, 3x^2 yz \)

---