How do I factorise 3xy^2 – 6xy fully?

When we factorise, we do so to make the expression more simple. Factorising is when we take common factors from the expression and group them together, and then multiply these common factors by something to produce the original expression.

 

In the given example of factorising the expression 3xy^2 - 6xy:

 

1) We start by looking for common factors. A common factor is a part of the expression that is included everywhere inside of the expression. We can see that 3, x and y are all common factors.

 

2) Now we have our common factors, we can move them to the front of our new expression and think about what we would need to multiply this by to achieve our original expression of 3xy^2 - 6xy.

 

3) Do this stage in parts, where the first part is the 3xy^2 and the second part is the -6xy.

What do we multiply 3xy by to get 3xy^2? We multiply by y

What do we multiply 3xy by to get -6xy? We multiply by -2

Now we can put this all together.

It should look like this:

3xy(y - 2)

And this is the fully factorised form.