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Expanding brackets is one of the fundamentals of algebra for GCSE Maths. There are two methods to learn. The first is expanding a single bracket and the second is expanding double brackets. Both methods are quite straightforward after a bit of practice. Take your time, read this guide carefully and then practice the questions at the bottom. If you have any questions then drop us a message and we can arrange a lesson with one of our expert maths tutors. You can also find out more here about the one-to-one tutoring we offer.

Expanding a single bracket

The clue is in the name with expanding brackets. You will be given an expression that includes brackets and asked to expand it. All you need to do is ensure you multiply all of the terms within the brackets by whatever is on the outside. Let’s look at an example…

Algebra - Expanding Brackets

Expanding Double Brackets

The hardest questions for expanding brackets will involve multiplying two sets of brackets together. You answer these sort of questions using the FOIL method. You need to make sure you multiply every term in the left hand bracket by every term in the right hand bracket. FOIL reminds you which terms you need to multiply to expand the bracket – it stands for: 

First

Outside

Inside

Last

Expanding double brackets

Practice Questions

Expand the following brackets: 

  • 2(x + 5)
  • 3(2a – 3)
  • 5(y + 3)
  • 4(3 – 2b)
  • 2a(2 + b)

Now try expanding these double brackets

  • (x + 3)(x + 4) 
  • (x + 2)(x – 5)
  • (a – 2)(a – 1)
  • (y + 6)(y – 5)

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