State whether a given pair of terms is like or unlike terms, 16,-45,4ab,6ba,-14x,-2y,9xy2,10bc,10b2c2

To determine whether a pair of terms is like or unlike, we must examine their variables and exponents. Terms are considered **like** if they have the same variables raised to the same powers, regardless of their coefficients. Otherwise, they are **unlike**.

Given the terms:
- \( 16 \)
- \( -45 \)
- \( 4ab \)
- \( 6ba \)
- \( -14x \)
- \( -2y \)
- \( 9xy^2 \)
- \( 10bc \)
- \( 10b^2c^2 \)

Now, let's compare them:

1. **\( 16 \) and \( -45 \)**:
   - Both are constants (no variables).
   - **Like terms.**

2. **\( 4ab \) and \( 6ba \)**:
   - Both have the same variables \( a \) and \( b \). The order of multiplication does not matter, so \( 4ab \) and \( 6ba \) are the same in terms of variables.
   - **Like terms.**

3. **\( -14x \) and \( -2y \)**:
   - \( -14x \) has the variable \( x \), and \( -2y \) has the variable \( y \). 
   - **Unlike terms.**

4. **\( 9xy^2 \) and \( 10bc \)**:
   - \( 9xy^2 \) has variables \( x \) and \( y^2 \), and \( 10bc \) has variables \( b \) and \( c \). 
   - **Unlike terms.**

5. **\( 10bc \) and \( 10b^2c^2 \)**:
   - \( 10bc \) has variables \( b \) and \( c \), while \( 10b^2c^2 \) has \( b^2 \) and \( c^2 \).
   - **Unlike terms.**

In summary, the pairs of terms that are like terms are:
- \( 16 \) and \( -45 \)
- \( 4ab \) and \( 6ba \)

All other pairs are unlike terms.

Would you like more details, or do you have any questions?

Here are some related questions to explore:

1. How do coefficients affect the classification of like terms?
2. Can terms with the same variables but different exponents be like terms?
3. What are some examples of like terms involving more complex expressions?
4. How do like and unlike terms impact simplification in algebraic expressions?
5. What role do like terms play in solving equations?

**Tip:** Always group like terms together when simplifying expressions or solving equations to make the process easier!

Learn how to determine whether terms in algebraic expressions are like or unlike. This detailed explanation covers examples such as constants, variables with different orders, and variables with different exponents. Suitable for students in Grades 6-8.

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