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.


Matthew H. GCSE Maths tutor

2 years ago

Answered by Matthew, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Marco-Iulian G. GCSE Maths tutor, Uni Admissions Test .MAT. tutor, A ...
£18 /hr

Marco-Iulian G.

Degree: Mathematics&Computer Science (Masters) - Bristol University

Subjects offered:Maths, Further Mathematics + 2 more

Further Mathematics

“I'm in my first year at University of Bristol, studying Mathematics and Computer Science MEng. From an early age I started to participate in lots of contests and maths olympiads, and the experience I achieved along the way enriched bo...”

£20 /hr

Rachael O.

Degree: Medicine (Other) - Bristol University

Subjects offered:Maths, Science+ 6 more

Human Biology
-Personal Statements-
-Medical School Preparation-

“Hi, my name's Rachael and I'm 21. I am a 3rd year medical student studying at Bristol University.  Availability: Mon-Fri 7pm-9pm (excluding Wednesdays). Weekends negotiable.  My aim is to help students enjoy learning and feel confid...”

£18 /hr

Killian D.

Degree: Mathematics (Bachelors) - Edinburgh University

Subjects offered:Maths, Physics+ 1 more


“Who am I? I am a first year Mathematics student in the University of Edinburgh. I am studying full time but have chosen to tutor as well as I have a passion for the subject; something I believe you will discover for yourself in our tu...”

About the author

Matthew H.

Currently unavailable: no new students

Degree: Mechanical Engineering (Masters) - Queen's, Belfast University

Subjects offered:Maths


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other GCSE Maths questions


Every past paper I sit, I miss an A* by a few marks. How do I ensure that I reach that top grade?

a) You area told that y is proportional to x2 and that when y = 75, x = 5. Find a formula for y in terms of x. y = x b) Find the value of y when x = 3. c) Find the value of x when y = 1200.

If x+y=100, x is a square number and y is a prime number, find the values of x and y.

View GCSE Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss