Factorise (i) x² + xy + 8x + 8y (ii) 15xy - 6x + 5y - 6 (iii) ax + by - ay - by (iv) 15pq + 15 + 9q + 25p (v) z + 7xy - xyz

(i) x² + xy + 8x + 8y = x(x + y) + 8(x + y) = (x + 8)(x + y)
(ii) 15xy - 6x + 5y - 6 = 3x(5y - 2) + 1(5y - 2) = (3x + 1)(5y - 2)
(iii) ax + by - ay - by = x(a + b) - y(a + b) = (x - y)(a + b)
(iv) 15pq + 15 + 9q + 25p = 3q(5p + 3) + 5(5p + 3) = (3q + 5)(5p + 3)
(v) z + 7xy - xyz = z(1 + 7xy - xy) = z(1 - xy)