Graduate Management Admission Test (GMAT) Practice Test

What is the expansion of the expression (x-y)²?

1. x² + y²

2. x² - 2xy + y²

3. (x-y)² = (x+y)(x-y)

4. 2xy

The correct answer is: x² - 2xy + y²

The expansion of the expression (x - y)² involves applying the formula for the square of a binomial. According to the binomial expansion rule, (a - b)² is equal to a² - 2ab + b². In this case, a corresponds to x and b corresponds to y. When applying this rule to (x - y)², we square the first term (x), multiply the first and second terms (x and y), and then square the second term (y). This leads to the following calculated parts: - The square of the first term: x² - The product of the two terms multiplied by 2 (with a minus sign because this is a subtraction): -2xy - The square of the second term: y² Combining these components together gives us the complete expansion: x² - 2xy + y². This accurately reflects the mathematical principles involved in expanding a squared binomial expression. Thus, the correct answer captures the essence of this expansion clearly and accurately.