The problem asks us to expand the expression $(x - y - 3)(x - y + 7)$.

1. Problem Description

The problem asks us to expand the expression $(x - y - 3)(x - y + 7)$.

2. Solution Steps

Let $u = x - y$. Then the expression becomes $(u - 3)(u + 7)$.

We can expand this expression using the distributive property (also known as FOIL):

$(u - 3)(u + 7) = u(u + 7) - 3(u + 7) = u^2 + 7u - 3u - 21 = u^2 + 4u - 21$.

Now we substitute $x - y$ back in for $u$:

$(x - y)^2 + 4(x - y) - 21 = (x^2 - 2xy + y^2) + (4x - 4y) - 21$.

Combining the terms, we get $x^2 - 2xy + y^2 + 4x - 4y - 21$.

3. Final Answer

$x^2 - 2xy + y^2 + 4x - 4y - 21$