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


£18 /hr

Joseph B.

Degree: Accounting and Finance (Bachelors) - LSE University

Subjects offered:Maths, Physics+ 1 more

-Personal Statements-

“Previously I have found that all pupils learn differently, so need to be taught differently, thus, tailoring my lessons to suit individuals.”

MyTutor guarantee

Daniel  M. GCSE Maths tutor, GCSE Physics tutor, GCSE Biology tutor, ...
£18 /hr

Daniel M.

Degree: Physics (Bachelors) - Bath University

Subjects offered:Maths, Science+ 4 more

-Personal Statements-

“Hi! I'm Daniel! As a patient, understanding, and industrious tutor, I aim to nourish your child's academic curiosity in a caring, understandable and encouraging manner so that they may be the best that they can be. I'm currently readi...”

£18 /hr

Susanna C.

Degree: Dentistry (Bachelors) - Newcastle University

Subjects offered:Maths, Chemistry+ 4 more

-Personal Statements-
-Medical School Preparation-

“Fun, hardworking Dental student from Newcastle University with previous mentoring experience. ”

MyTutor guarantee

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

How to find the roots of a Quadratic Equation by Factorising?

Solve the following set of simultaneous equations: 3x + 2y = 15 & 9x + 4y = 1

How do you differentiate? And how is integration related to it?

How would I go about drawing a graph if i had no idea how to start?

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