Which of the following is a like term of x²?
Answer and explanation
Correct answer: 3x²
Like terms must have exactly the same variables raised to the same powers; only their numerical coefficients may differ. The term x² has variable x with exponent 2. In 3x², the variable part is also x², and the coefficient 3 may differ from the implicit coefficient 1 in x². Therefore 3x² is a like term, making option A correct. The term 3x has exponent 1, so it is unlike. x³ has the same variable but a different exponent, so it is also unlike. Finally, 2y² uses a different variable, y, and cannot be combined with x². The rule concerns the literal variable-and-exponent pattern, not merely the numerical coefficient or the appearance of a square.
Frequently asked questions
What is the correct answer to this question?
3x²
Why is this the correct answer?
Like terms must have exactly the same variables raised to the same powers; only their numerical coefficients may differ. The term x² has variable x with exponent 2. In 3x², the variable part is also x², and the coefficient 3 may differ from the implicit coefficient 1 in x². Therefore 3x² is a like term, making option A correct. The term 3x has exponent 1, so it is unlike. x³ has the same variable but a different exponent, so it is also unlike. Finally, 2y² uses a different variable, y, and cannot be combined with x². The rule concerns the literal variable-and-exponent pattern, not merely the numerical coefficient or the appearance of a square.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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