Find the difference.
$3 x^2 y-x^2 y$
A. 2
B. $2 x^2 y$
C. $3 x^2 y$
D. $4 x^2 y

Identify the like terms: 3 x 2 y and x 2 y .
Subtract the coefficients: 3 − 1 = 2 .
Write the result with the common variable part: 2 x 2 y .
The difference is 2 x 2 y ​ .

Explanation

Understanding the Problem We are asked to find the difference between 3 x 2 y and x 2 y . These are like terms, meaning they have the same variables raised to the same powers. To find the difference, we subtract the coefficients of the like terms.

Subtracting the Coefficients The coefficient of 3 x 2 y is 3, and the coefficient of x 2 y is 1. Subtracting the coefficients, we have: 3 − 1 = 2

Writing the Result Now, we write the result with the common variable part, which is x 2 y . Therefore, the difference is 2 x 2 y .


Examples
Understanding how to combine like terms is fundamental in many areas, such as simplifying algebraic expressions, solving equations, and modeling real-world scenarios. For example, if you have 3 boxes each containing x 2 y number of apples and you give away one such box, you are left with 3 x 2 y − x 2 y = 2 x 2 y apples. This concept is also used in physics to combine forces or in economics to aggregate quantities.

Answered by GinnyAnswer | 2025-07-03

The difference between 3 x 2 y and x 2 y is found by subtracting the coefficients of the like terms. This results in 2 x 2 y . Therefore, the correct choice is B .2 x 2 y .
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Answered by Anonymous | 2025-07-04