In each polynomial, given below, separate the like terms :
`3xy - 4yx^(2), 2xy^(2), 2.5x^(2)y, 8yx, -3.2 y^(2)x` and `x^(2)y`

Answer

To separate the like terms in the given polynomial, we will identify terms that have the same algebraic factors. The given polynomial is:

\[ 3xy - 4yx^2 + 2xy^2 + 2.5x^2y + 8yx - 3.2y^2x + x^2y \]

### Step-by-Step Solution:

1. **Identify the Terms**:
The polynomial consists of the following terms:
- \( 3xy \)
- \( -4yx^2 \)
- \( 2xy^2 \)
- \( 2.5x^2y \)
- \( 8yx \)
- \( -3.2y^2x \)
- \( x^2y \)

2. **Group the Like Terms**:
- **Like Terms with \( xy \)**:
- \( 3xy \)
- \( 8yx \) (Note: \( yx \) is the same as \( xy \))
- **Like Terms with \( x^2y \)**:
- \( -4yx^2 \) (which can be written as \( -4x^2y \))
- \( 2.5x^2y \)
- \( x^2y \)
- **Like Terms with \( xy^2 \)**:
- \( 2xy^2 \)
- **Like Terms with \( y^2x \)**:
- \( -3.2y^2x \) (which can be written as \( -3.2xy^2 \))

3. **Write the Grouped Terms**:
- The grouped like terms are:
- For \( xy \): \( 3xy + 8xy \)
- For \( x^2y \): \( -4x^2y + 2.5x^2y + x^2y \)
- For \( xy^2 \): \( 2xy^2 \)
- For \( y^2x \): \( -3.2y^2x \)

4. **Final Grouping**:
- Combine the like terms:
- \( (3xy + 8xy) \) gives \( 11xy \)
- \( (-4x^2y + 2.5x^2y + x^2y) \) gives \( (-4 + 2.5 + 1)x^2y = -0.5x^2y \)
- \( 2xy^2 \) remains as is.
- \( -3.2y^2x \) remains as is.

### Final Answer:
The separated like terms are:
- \( 11xy \)
- \( -0.5x^2y \)
- \( 2xy^2 \)
- \( -3.2y^2x \)