Question

Identify the like terms in the in the following algebraic expressions: $abc+a{{b}^{2}}c+3{{c}^{2}}ab+{{b}^{2}}ac-2{{a}^{2}}bc+3ca{{b}^{2}}$

Answer 1

Hint: We know that all those terms in which the variables are the same and their respective exponents are also the same, then the terms are called like terms. And all those terms which are not like terms are called unlike terms. Using this definition, we can list all like terms in the given expression.

Complete step-by-step solution:
We know that there are two types of terms in any algebraic expression. These are called like terms and unlike terms.
We know that the terms in which all the variables are the same and respective variables have the exactly the same exponent, then the terms are called like terms.
And all those terms which are not like terms are called unlike terms.
For example, we can say that the terms $xy$ and $yx$ are like terms, and the terms $xy$ and ${{x}^{2}}$ are unlike terms.
We have the following given expression, $abc+a{{b}^{2}}c+3{{c}^{2}}ab+{{b}^{2}}ac-2{{a}^{2}}bc+3ca{{b}^{2}}$.
In this expression, we can see that the term $a{{b}^{2}}c$, the term ${{b}^{2}}ac$ and the term $ca{{b}^{2}}$ are like terms, as in all of these terms, the exponent of a is 1, the exponent of b is 2 and the exponent of c is also 1.
Also, we can see that there are no other like terms in this expression.
Hence, we can say that the terms $a{{b}^{2}}c$, ${{b}^{2}}ac$ and $3ca{{b}^{2}}$ are like terms in this given expression.

Note: We must observe carefully that the coefficient and the sign of these terms are neglected while selecting like terms. We must know that the significance of like terms is that it simplifies any given expression and makes it easier to solve.