The distributive law means to multiply the coefficient (number/letters outside of the brackets) by all of the contents inside of the brackets.

In this case, the coefficient is k and I’m going to multiply it by “a” and “b”, which gives me a new expression of ka + kb.

Factorising is the opposite action of expanding brackets.

The first step to help you factorise common algebraic factors is to break each individual term into expanded form.

In this scenario, we know that 3xy^2 can be expanded into 3 x (x) x (y) x (y).

12x^2y can be expanded into 12 x x x x x y or if I want to go even further I can go 2 x 2 x 3 x (x) x (x) x (y).

Now if you look at both lists, 3 x (x) x (y) is common between both lists, so they can not be removed to the outside of the brackets, leaving everything else inside the brackets.

3xy(y + 4x)