We use standard algebraic identities to find the products without direct multiplication. For (i) and (vi), we use the identity (a - b)^2 = $a^{2}$ - 2ab + $b^{2}$ or (a + b)^2 = $a^{2}$ + 2ab + $b^{2}$. For (ii), (iii), and (iv), we use the difference of squares identity (a + b)(a - b) = $a^{2}$ - $b^{2}$. For (v), we use the identity (x - y)($x^{2}$ + xy + $y^{2}$) = $x^{3}$ - $y^{3}$. For (vii), we use (a + b + c)^2 = $a^{2}$ + $b^{2}$ + $c^{2}$ + 2ab + 2bc + 2ca. For (viii), we use (a - b)^3 = $a^{3}$ - $3a^{2b}$ + $3ab^{2}$ - $b^{3}$.