The problem is to expand the expression $(x-y)^2$.

AlgebraAlgebraic ExpansionBinomial TheoremPolynomials
2025/3/12

1. Problem Description

The problem is to expand the expression (xy)2(x-y)^2.

2. Solution Steps

We need to expand (xy)2(x-y)^2. This is a binomial squared. We can use the formula:
(ab)2=a22ab+b2(a-b)^2 = a^2 - 2ab + b^2
Applying this formula to (xy)2(x-y)^2 where a=xa=x and b=yb=y, we get:
(xy)2=x22(x)(y)+y2(x-y)^2 = x^2 - 2(x)(y) + y^2
(xy)2=x22xy+y2(x-y)^2 = x^2 - 2xy + y^2

3. Final Answer

x22xy+y2x^2 - 2xy + y^2