Question

State whether a given pair of terms are like or unlike terms.
(1) \[1,100\]
(2) \[-7x,\dfrac{5}{2}x\]
(3) \[-29x,-29y\]

Answer 1

Hint: We are given a question based on like and unlike terms. We have to tell whether the pair in each of the sub-parts are like terms or unlike terms. Like terms refers to those terms which have same variables and powers and similar literal coefficients and unlike terms refers to those which have different variables and powers. Based on this information, we will get whether the pair is like or unlike. Hence, we will have the required answers.

Complete step by step answer:
According to the given question, we are asked to state whether the pairs given in each of the sub – parts are like terms or unlike terms.
We know that, like terms refers to those terms which have same variables and powers and similar literal coefficients and unlike terms refers to those which have different variables and powers. For example – 3xy and 5yx are similar as they have similar variables and have similar powers.
And unlike terms refer to those which have different variables and powers.
For example – 3xy and 3xz are unlike terms as the variables are different.
Firstly, we have,
(1) \[1,100\]
Here, 1 and 100 both belong to the set of natural numbers and so the pair has like terms.
Next, we have,
(2) \[-7x,\dfrac{5}{2}x\]
Here, both the terms have the same variables and the literals belong to the set of real numbers. So, the pair has like terms.
Next, we got,
(3) \[-29x,-29y\]
In this pair, we have the terms with different variables and so the pair has unlike terms.

Note: The like terms and unlike terms should not be confused. In order to check the likeness of the terms, begin with the variables first. If the variables are same then there is a chance that the pair has like terms else, we can write the pair has unlike terms. The next thing to be checked is the powers and then proceed onto literal values.