Select all the like terms in the following expression

To identify the like terms in the expression \( 3x^4 - 8x^2 + 9y + 10xy + 7x^2 - xy + 8z \), we need to group the terms based on their variables and exponents.

Here's the breakdown:

- \( 3x^4 \) is a term by itself since it contains \( x^4 \).
- \( -8x^2 \) and \( 7x^2 \) are like terms since they both contain \( x^2 \).
- \( 9y \) is a term by itself as it contains \( y \).
- \( 10xy \) and \( -xy \) are like terms since they both contain the product \( xy \).
- \( 8z \) is a term by itself, as it contains \( z \).

Based on this categorization, the like terms are:

- \( -8x^2 \) (option b)
- \( 7x^2 \) (option e)
- \( 10xy \) (option d)
- \( -xy \) (option g)

So, the selected like terms are:

- **b**: -8x2
- **e**: 7x2
- **d**: 10xy
- **g**: -xy

The options can be combined with their like terms:

1. **-8x²**
2. **7x²**
3. **10xy**
4. **-xy**

These terms can be combined or simplified in the context of further algebraic manipulation.