Factorise:

(i) $x^{3}-3 x^{2}+x-3$

$=x^{2}(x-3)+1(x-3)$

$=\left(x^{2}+1\right)(x-3)$

(ii) $63 x^{2} y^{2}-7$

$=7\left(9 x^{2} y^{2}-1\right)$

$=7\left((3 x y)^{2}-(1)^{2}\right)$       [according to the formula $a^{2}-b^{2}=(a+b)(a-b)$ ]

$=7(3 x y+1)(3 x y-1)$

(iii) $1-6 x+9 x^{2}$

$=9 x^{2}-6 x+1$

$=9 x^{2}-3 x-3 x+1$

$=3 x(3 x-1)-1(3 x-1)$

$=(3 x-1)(3 x-1)$

$=(3 x-1)^{2}$

$($ iv $) 7 x^{2}-19 \mathrm{x}-6$

$=7 x^{2}-21 x+2 x-6$

$=7 x(x-3)+2(x-3)$

$=(7 x+2)(x-3)$