(1) To multiply using the distributive property, we multiply each term of the first expression by the entire second expression. (x - y)($x^{2}$ + xy + $y^{2}$) = x($x^{2}$ + xy + $y^{2}$) - y($x^{2}$ + xy + $y^{2}$) = $x^{3}$ + $x^{2y}$ + $xy^{2}$ - $x^{2y}$ - $xy^{2}$ - $y^{3}$ Combining the like terms, the middle terms cancel out, leaving $x^{3}$ - $y^{3}$.

(2) Similarly, applying the distributive property to the second expression: (x + y)($x^{2}$ - xy + $y^{2}$) = x($x^{2}$ - xy + $y^{2}$) + y($x^{2}$ - xy + $y^{2}$) = $x^{3}$ - $x^{2y}$ + $xy^{2}$ + $x^{2y}$ - $xy^{2}$ + $y^{3}$ Combining the like terms, the middle terms cancel out, resulting in $x^{3}$ + $y^{3}$.