1. Factorise $ax - ay$: $$ax - ay = a(x - y)$$ 2. Factorise $5ax^2 - 35ay^2 + 45az^2$: $$5ax^2 - 35ay^2 + 45az^2 = 5a(x^2 - 7y^2 + 9z^2)$$ 3. Factorise $x(2x - y) + y(2x - y)$: $$x(2x - y) + y(2x - y) = (x + y)(2x - y)$$ 4. Factorise $3x(a + 1) + (a + 1)$: $$3x(a + 1) + (a + 1) = (3x + 1)(a + 1)$$ 5. Factorise $4a(x + 3) - 2(x + 3)$: $$4a(x + 3) - 2(x + 3) = (4a - 2)(x + 3)$$ 6. Factorise $3x^2(a - 2) - 6x(a - 2)$: $$3x^2(a - 2) - 6x(a - 2) = 3x(a - 2)(x - 2)$$ 7. Factorise $x^2 + 10x + 25$: $$x^2 + 10x + 25 = (x + 5)^2$$ 8. Factorise $x^2 - 12x + 36$: $$x^2 - 12x + 36 = (x - 6)^2$$