Question

Which of the following is a pair of unlike algebraic terms?
A) $ - pqr, 0.8qrp$
B) ${a^2}bc, - 6b{a^2}c$
C) $1.5xzy, 3xyz$
D) $ - kmn, 48kml$

Answer 1

Hint:
Here, it is asked to find the unlike algebraic terms from the terms given in the options.
The definition of unlike algebraic terms is stated as “The terms which have either different variables or are with different exponents or both are called unlike terms”.
Thus, find the terms which show the above property which will result in the required answer.

Complete step by step solution:
In the given question, we are asked to find unlike terms from the given terms in each of the options.
So, first we need to understand the difference between like and unlike algebraic terms.
Like algebraic terms: The terms which have same variables also with same exponents but are co-efficient are different are called like terms.
Unlike algebraic terms: The terms which have either different variables or are with different exponents or both are called unlike terms.
So, we need to find the option whose terms show one or both of the properties of unlike terms.
In option (A), the terms given are $ - pqr,0.8qrp$ . So, the variables in the terms are the same i.e. p, q and r. Also, the coefficient of first term is -1 and that of second term is 0.8. So, the given terms are like terms. Thus, option (A) is not the required answer.
In option (B), the terms given are ${a^2}bc, - 6b{a^2}c$ . So, the variables in the terms are the same i.e. ${a^2}$ , b and c. Also, the coefficient of first term is 1 and that of second term is -6. So, the given terms are like terms. Thus, option (B) is not the required answer.
In option (C), the terms given are $1.5xzy,3xyz$ . So, the variables in the terms are the same i.e. x, y and z. Also, the coefficient of first term is 1.5 and that of second term is 3. So, the given terms are like terms. Thus, option (C) is not the required answer.
In option (A), the terms given are $ - kmn,48kml$ . So, the variables in the terms are not the same i.e. variables of the first term are k, m and n, while that of the second term are k, m and l. Although, the exponents of the variables are the same, the given terms show one property of unlike terms. So, the given terms are like terms. Thus, option (D) is the required answer.

So, option (D) is the correct answer.

Note:
Terms:
Before learning like and unlike terms, we must first understand what term is.
In algebra, terms are the values on which mathematical operators like addition, subtraction, multiplication and division can be performed in an expression. Also, a term can be a variable or a constant or can be both in an expression.
For example, in the expression 7x + 2, 7x and 8 are terms in which x is the variable.