Yes, we can clearly see that x - y is a factor of $x^{4}$ - $y^{4}$ by using algebraic identities.

First, we can express $x^{4}$ - $y^{4}$ as the difference of two squares: ($x^{2}$)^2 - ($y^{2}$)^2. Using the identity for the difference of squares, this becomes ($x^{2}$ - $y^{2}$)($x^{2}$ + $y^{2}$).

We already know from the identity $x^{2}$ - $y^{2}$ = (x - y)(x + y) that $x^{2}$ - $y^{2}$ contains (x - y) as a factor. By substituting this into our previous expression, we get $x^{4}$ - $y^{4}$ = (x - y)(x + y)($x^{2}$ + $y^{2}$). This directly shows that x - y is a factor of $x^{4}$ - $y^{4}$.