Question

Group the like terms together: \[9{x^2},xy, - 3{x^2},{x^2} - 2xy\]

Answer 1

Hint: A symbol having a fixed value is known as constant and a symbol that takes various values is called variables. The combination of variables and constants with the basic four arithmetic operations is called an algebraic equation. The parts of algebraic equations separated by \[ + \] or \[ - \]are called terms. The terms having similar variables are called similar terms or like terms. Here we will separate the terms having the same variables.

Complete step by step answer:
The given terms are \[9{x^2},xy, - 3{x^2},{x^2} - 2xy\]. The last one is an algebraic expression having two terms. They are \[{x^2}\] and \[ - 2xy\]. Thus, we have five terms: they are \[9{x^2},xy, - 3{x^2},{x^2}, - 2xy\].
Now let us separate them. By the definition of the like term, we know that terms having similar variables are known as like terms.
Let us take the first term, \[9{x^2}\] here the constant is \[9\] and the variable is \[{x^2}\].
Now the third term, \[ - 3{x^2}\] here the constant is \[ - 3\] and the variable is \[{x^2}\].
Let us take the fourth term, \[{x^2}\] here the constant is \[1\] and the variable is \[{x^2}\].
Thus,\[9{x^2}, - 3{x^2},{x^2}\] are like terms since they have similar variables \[{x^2}\].
Now let us take the second term, \[xy\] here the constant is \[1\]and the variable is \[xy\].
Let us take the fifth term, \[ - 2xy\] here the constant is \[ - 2\]and the variable is \[xy\].
Again, by the definition of the like term, we know that terms having similar variables are known as like terms.
Thus, \[xy, - 2xy\] are like terms.
Hence, we got two sets of the like term: (1) \[9{x^2}, - 3{x^2},{x^2}\] with the variable \[{x^2}\]and (2) \[xy, - 2xy\] with the variable \[xy\].

Note: We know that the terms having the same or similar variables are called like or similar terms. Also, the terms having different variables are known as, unlike terms. Thus, we need to first separate the given terms then we will group them according to their variables.