What is the variable part in (12x^2y)?

(x^2y)

A term in algebra can be separated into its numerical coefficient and its variable part. In \(12x^2y\), the number 12 tells how many times the variable product is taken, so 12 is the coefficient. The letters and their powers together form the variable part. Hence the variable part is \(x^2y\), making option B correct. The exponent 2 belongs to x, while y has an understood exponent of 1.

To verify this, rewrite the term as \(12\times x^2\times y\). The first factor is numerical, and the remaining factors contain variables, so they form the variable part. Option A names only the coefficient. Option C contains both a number and a variable, so it is not the complete variable part. Option D leaves out \(x^2\). Therefore, separating the term into coefficient and literal or variable factors leads to option B.

This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Algebraic expressions.