Factorise fully, question

(x-1)² -9(y-1)²

9(y-1)^2 = (3y-3)^2
Now use the following formula for factorisation
(a^2-b^2)=(a+b)(a-b)
(x-1)^2 - (3y-3)^2
= (x-1+3y-3)(x-1-3y+3)
= (x+3y-4)(x-3y+2)

(x-1)² -9(y-1)² =
((x - 1) + 3(y - 1))((x - 1) - 3(y - 1)) =
(x + 3y - 4)(x - 3y + 2)