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:
- -8x²
- 7x²
- 10xy
- -xy
These terms can be combined or simplified in the context of further algebraic manipulation.
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