Question

Find the like terms of \[3xy\].
\[(a)\,2xy\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(b)\,\,5xy\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(c)\,\,7xy\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(d)\,\,All\,\,of\,these\]

Answer 1

Hint: Like terms are those having the same group of variables. By matching the variables of a given term with all the options we will get the answer.

Complete step by step answer:
(1) Given term is\[3xy\].
Here we see that term \[3xy\] having a variable $x\, and \,y$ or group of variables \[\left( {xy} \right)\] .
(2) Therefore, all terms which do have variable $x$ and $y$ or group \[\left( {xy} \right)\] as variables will be considered as terms.
(3) On seeing in options given in
Option (a)\[\;2xy\]
Option (b) \[5xy\]
Option (c) \[7xy\]
We see that terms in options \[a,{\text{ }}b{\text{ }}and{\text{ }}c\] have the same group that is the same as the given term.
So, we can say that option a, option b and option c have like terms of \[3xy\].

Therefore, option d (all of these) is the correct option.

Additional Information: In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.

Note: Like terms have the same group of variables (or equal number of variable powers).