How do I expand (3x + 6)(x + 2) ?

Firstly, this is a classic GCSE question that crops up time and again, so it's worth making sure that you can expand brackets blindfolded and with your arms tied behind your back before you walk into the exam. These can be easy marks in the bag every time and once you've got the hang of it, they're not too difficult.

The trick to expanding brackets is to always remember FOIL. That's First, Outside, Inside and Last. Now what does that mean? I hear you ask. Well each of the letters in FOIL refer to a different pair of numbers in the bracket.

The F stands for First. What this means is that you need to multiply the first numbers in the brackets together. The first thing in the first bracket is 3x and the first thing in the second bracket is x, so multiply these together to get 3x^2.

The O stands Outside. If we think of the brackets together now, we can see that there are two things on the outside of the brackets, and that is the 3x and the 2. We now multiply these together to get 6x.

The I stands for Inside. Just as we did for the Outside numbers, we imagine the two brackets as one thing, but this time we take the two Inside numbers. In our example, this is 6 and x. Multiply these two together to get 6x.

Finally, L stands for Last. Remember when we multiplied the the First two numbers in each bracket together? Now we just multiply the Last two numbers in each bracket together. Here they are 6 and 2, so we multiply them to get 12.

Now we have our four numbers, we simply add them all together to get our result:

(3x + 6)(x + 2) = F + O + I + L

=3x^2 + 6x + 6x + 12

=3x^2 + 12x + 12

That's the trick to expanding brackets. Just follow the simple steps every time and you've got full marks every time!

Joshua B. GCSE Maths tutor, A Level Maths tutor, A Level Further Math...

1 year ago

Answered by Joshua, a GCSE Maths tutor with MyTutor

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


£22 /hr

Thomas D.

Degree: Neuroscience (Bachelors) - Kings, London University

Subjects offered:Maths, Science+ 3 more


“I am currently in my second year of a Neuroscience Bachellors' degree at a Russel Group institution, that is King's College London. Having done five (yes 5) A2s, and achieved an A* and 5 As, I know a few tricks of the trade so to spea...”

£20 /hr

Guy P.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics + 2 more

Further Mathematics

“Hi there. Thank you for taking the time to visit my profile, it would be great to meet in a FREE 15-minute meeting! I look forward to hearing from you soon!”

£18 /hr

Ayyub A.

Degree: Mathematics Msci (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics + 1 more

Further Mathematics

“Hi I'm Ayyub, current student at Bristol university studying Maths. I have significant tutoring experience in maths and hopefully i'll be able to help you out.”

About the author

£24 /hr

Joshua B.

Degree: Mathematics (Masters) - Durham University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“Hi! I’m Josh, a third year on a four-year Mathematics course. I got 100% in both my Maths IGCSE and A-Level, and did all 18 A-Level modules.”

You may also like...

Other GCSE Maths questions

Solve the following for X and Y: 2y+4x=14 and x-y=-1

Express 300 as a product of its prime factors.

Factorise 4xy-6xz

How do I add two fractions? (plus example)

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