Factorize the expression x² + 2xy + y² - a².

Recognize the first three terms as a perfect square trinomial: $x^2 + 2xy + y^2 = (x+y)^2$.
The expression becomes:

$$(x+y)^2 - a^2$$

This is a difference of squares, $A^2 - B^2 = (A-B)(A+B)$, where $A = (x+y)$ and $B = a$.

$$(x+y-a)(x+y+a)$$

The factored form is $\boxed{(x+y-a)(x+y+a)}$.