Why are (a^2b) and (ab^2) not like terms?
Answer and explanation
Correct answer: Because powers of (a) and (b) are arranged differently
Like terms are algebraic terms that have exactly the same variables with exactly the same exponents. Their coefficients may be different, but the variable pattern must match. In \(a^2b\), the exponent of a is 2 and the exponent of b is 1. In \(ab^2\), the exponent of a is 1 and the exponent of b is 2. The exponents are therefore interchanged, so the terms are not like terms. Option C states this idea.
The terms may look similar because both contain a and b, but merely having the same letters is not enough. For example, \(3a^2b\) and \(-5a^2b\) are like terms, while \(a^2b\) and \(ab^2\) are not. Options A, B and D do not describe the actual difference: the coefficients need not be the issue, variables are present, and these are not constants. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
Because powers of (a) and (b) are arranged differently
Why is this the correct answer?
Like terms are algebraic terms that have exactly the same variables with exactly the same exponents. Their coefficients may be different, but the variable pattern must match. In \(a^2b\), the exponent of a is 2 and the exponent of b is 1. In \(ab^2\), the exponent of a is 1 and the exponent of b is 2. The exponents are therefore interchanged, so the terms are not like terms. Option C states this idea.
The terms may look similar because both contain a and b, but merely having the same letters is not enough. For example, \(3a^2b\) and \(-5a^2b\) are like terms, while \(a^2b\) and \(ab^2\) are not. Options A, B and D do not describe the actual difference: the coefficients need not be the issue, variables are present, and these are not constants. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Algebraic expressions.
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