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

1 year ago

Answered by Matthew, a GCSE Maths tutor with MyTutor

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


PremiumVandan P. Mentoring -Oxbridge Preparation- tutor, A Level Physics tut...
View profile
£24 /hr

Vandan P.

Degree: Physical Natural Sciences (Bachelors) - Cambridge University

Subjects offered: Maths, Science+ 6 more

Further Mathematics
-Oxbridge Preparation-

“I am a second year undergraduate at Corpus Christi College Cambridge. I am studying Natural Sciences. In my first year I did Physics, Chemistry, Computer Science and Maths and passed with first class honours....”

PremiumMatthew K. GCSE Maths tutor, GCSE Physics tutor
View profile
£22 /hr

Matthew K.

Degree: General Engineering (Masters) - Warwick University

Subjects offered: Maths, Physics


“About MeI am a student studying a general engineering masters degree at Warwick University. I amfun and friendly and have a passion for maths and physics with a little bit of rugby on the side.I helped my brother whilst he was ...”

PremiumOctavia C. A Level History tutor, GCSE History tutor, GCSE Maths tuto...
View profile
£24 /hr

Octavia C.

Degree: History (Bachelors) - Durham University

Subjects offered: Maths, Politics+ 2 more

English Literature

“About Me:  My name is Octavia Cogher and I am in my second year studying history at Durham University. I am interested in a broad range of topics and periods, but particularly in twentieth-century political history. Last year, I tuto...”

About the author

Matthew H. GCSE Maths tutor
View profile

Matthew H.

Currently unavailable: no new students

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

Subjects offered: Maths


“Matt, 20 Years Old, Mechanical Engineering Student”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Solve the equations giving your answer in 2d.p (5 Marks).: x^2 + y^2 = 36 , x = 2y + 6

Factorise 2c2 + 8c + 8.

How do you factorise a quadratic equation?

How do I solve the quadratic equation x^2+4x+3=0

View GCSE Maths tutors


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