We are asked to simplify the expression $(x - y)[(2x+y)-(-2y+x)]$.

1. Problem Description

We are asked to simplify the expression $(x - y)[(2x+y)-(-2y+x)]$.

2. Solution Steps

First, simplify the expression inside the square brackets.

$(2x+y)-(-2y+x) = 2x+y+2y-x$

Combining like terms, we have:

$2x - x + y + 2y = x + 3y$

So the expression becomes $(x-y)(x+3y)$.

Next, expand the expression using the distributive property:

$(x-y)(x+3y) = x(x+3y) - y(x+3y)$

$= x^2 + 3xy - xy - 3y^2$

Combine like terms:

$x^2 + 3xy - xy - 3y^2 = x^2 + 2xy - 3y^2$

3. Final Answer

$x^2 + 2xy - 3y^2$