IGCSEMathsEdexcelMaths BRevision NotesAlgebraExpanding BracketsExpanding Double Brackets

Expanding Double Brackets (Edexcel IGCSE Maths B): Revision Note

Exam code: 4MB1

Written by: Mark Curtis

Reviewed by: Dan Finlay

Updated on 19 January 2026

Expanding two brackets

How do I expand two brackets?

Every term in the first bracket must be multiplied by every term in the second bracket
- Expanding (x + 1)(x + 3) requires 4 multiplications in total
  - x(x + 1) + 3(x + 1)
  - x×x + 1x + 3x + 3
  - x² + 4x + 3

Using a grid

You can use a grid for a visual way to expand brackets
To expand (x + 1)(x + 3), write out the brackets as row and column headings of a grid
- They can be in either direction
- Remember to write the appropriate sign in front of each term
x
+1
x

+3
For each cell in the grid, multiply the term in the row heading by the term in the column heading
x
+1
x
x²
x
+3
3x
3
Add together all the terms inside the grid to get the answer
- x² + x + 3x + 3
Collect like terms
x² + 4x + 3

Using FOIL

Every term in the first bracket must be multiplied by every term in the second bracket
- Expanding (x + 1)(x + 3) requires 4 multiplications in total
A good way to remember all the multiplications is FOIL
- F = First: multiply together the first terms in each bracket
- O = Outside: multiply the first term in the first bracket by the last term in the last bracket
  - Visually, these are the outer terms
- I = Inside: multiply the last term in the first bracket by the first term in the last bracket
  - Visually, these are the inner terms
- L = Last: multiply together the last terms in each bracket
It helps to put negative terms in brackets when multiplying
Simplify the final answer by collecting like terms (if there are any)

How do I expand when there are multiple variables?

All the same rules and methods apply as when there is just one variable
Remember to only simplify like terms
For example: $(3 x + 2 y) (4 x - 6 y)$
- Expanding: $12 x^{2} - 18 x y + 8 x y - 12 y^{2}$
- The $x y$ terms can be combined
- $12 x^{2} - 10 x y - 12 y^{2}$

Worked Example

(a) Expand $(2 x - 3) (x + 4)$ .

Answer:

Using FOIL, multiply together the first, outer, inner and last terms

$F O I L 2 x \times x + 2 x \times 4 + (- 3) \times x + (- 3) \times 4$

Simplify each term

$2 x^{2} + 8 x - 3 x - 12$

Collect like terms (the 8x and -3x)

$2 x^{2} + 5 x - 12$

(b) Expand $(x - 3) (3 x - 5)$ .

Answer:

Using FOIL, multiply together the first, outer, inner and last terms

$F O I L x \times 3 x + x \times (- 5) + (- 3) \times 3 x + (- 3) \times (- 5)$

Simplify each term

$3 x^{2} - 5 x - 9 x + 15$

Collect like terms (the -5x and -9x)

$3 x^{2} - 14 x + 15$

Worked Example

Expand $(3 r + 2 t) (5 t - 8 r)$ .

Answer:

Expand using your chosen method, here we will use a grid

	$3 r$	$+ 2 t$
$5 t$
$- 8 r$

Work out the term in each place in the grid by multiplying

	$3 r$	$+ 2 t$
$5 t$	$15 r t$	$10 t^{2}$
$- 8 r$	$- 24 r^{2}$	$- 16 r t$

So the expanded expression is

$10 t^{2} + 15 r t - 16 r t - 24 r^{2}$

The $r t$ terms can be combined

$10 t^{2} - r t - 24 r^{2}$

Expanding squared brackets

How do I expand a bracket squared?

Remember that a square number is a number multiplied by itself
Write (x + 3)² as (x + 3)(x + 3) and use one of the methods above
- With FOIL: (x + 3)(x + 3) = x²+ 3x + 3x + 9
- Then collect like terms: x² + 6x + 9

Examiner Tips and Tricks

Do not make the common mistake of saying ${(x + y)}^{2}$ is the same as $x^{2} + y^{2}$ . In general, this is not true.

Worked Example

Expand ${(2 x + 3)}^{2}$ .

Answer:

Remember that the answer is not (2x)² + 3²
Rewrite the expression as two separate brackets multiplied together

$(2 x + 3) (2 x + 3)$

Using FOIL, multiply together the first, outer, inner and last terms

$F O I L 2 x \times 2 x + 2 x \times 3 + 3 \times 2 x + 3 \times 3$

Simplify each term

$4 x^{2} + 6 x + 6 x + 9$

Collect like terms (the 6x and 6x)

$4 x^{2} + 12 x + 9$

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

I would just like to say a massive thank you for putting together such a brilliant, easy to use website.I really think using this site helped me secure my top gradesin science and maths. You really did save my exams! Thank you.

Beth
IGCSE Student

This website is soooo useful and I can’t ever thank you enough for organising questions by topic like this. Furthermore, the name of the website could not have been more appropriate as it literally did SAVE MY EXAMS!

Fathima
A Level Student

Incredible! SO worth my money, the revision notes have everything I need to know and are so easy to understand. I actually enjoy revising! It makes me feel a lot more confident for my GCSEs in a few months.

Kate
GCSE Student

Absolutely brilliant, both my girls used it for A levels and GCSE. It's saves on paper copies, also beneficial exam questions ranked from easy to hard. It's removed a lot of stress from the exams.

Sameera
Parent

Just to say that your resources are the best I have seen and I have been teaching chemistry at different levels for about 40 years

Mark
Chemistry Teacher

Excellent

Expanding Double Brackets (Edexcel IGCSE Maths B): Revision Note

Expanding two brackets

How do I expand two brackets?

Using a grid

Using FOIL

How do I expand when there are multiple variables?

Worked Example

Worked Example

Expanding squared brackets

How do I expand a bracket squared?

Examiner Tips and Tricks

Worked Example

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

Author: Mark Curtis

Reviewer: Dan Finlay

	x	+1
x	x²	x
+3	3x	3