a) x$^{2}$ - 9 + (x – 3)$^{2}$ = (x – 3)(x + 3) + (x – 3)$^{2}$ = (x – 3)[(x + 3) + (x – 3)] = 2x(x – 3);            

b) x$^{3}$ - 4x$^{2}$ + 4x - xy$^{2}$ = x(x$^{2}$ - 4x + 4 - y$^{2}$) = x[(x – 2)$^{2}$ - y$^{2}$] = x(x – 2 – y)(x – 2 + y);

c) x$^{3}$ - 4x$^{2}$ + 12x – 27 = x$^{3}$ - 3x$^{2}$ - x$^{2}$ + 3x + 9x – 27

                                    = x$^{2}$(x – 3) – x(x – 3) + 9(x - 3) = (x – 3)(x$^{2}$ - x + 9);                                  

d) 3x$^{2}$ - 7x – 10 = 3x$^{2}$ + 3x – 10x – 10 = 3x(x + 1) – 10(x + 1) = (x + 1)(3x – 10);

e) 5x$^{3}$ - 5x$^{2}$y – 10x$^{2}$ + 10xy = 5x$^{2}$(x – y) – 10x(x – y) = (x – y)(5x$^{2}$ - 10x);               

f) 3x$^{2}$ - 6xy + 3y$^{2}$ - 12z$^{2}$ = 3(x$^{2}$ - 2xy + y$^{2}$ - 4z$^{2}$) = 3[(x – y)$^{2}$ - (2z) $^{2}$] = 3(x – y – 2)(x – y + 2).