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Expand Products of Two Binomials

In this worksheet, students will use the FOIL (First - Outer - Inner - Last) method to expand and simplify double brackets.

'Expand Products of Two Binomials' worksheet

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA,

Curriculum topic:   Algebra

Curriculum subtopic:   Notation, Vocabulary and Manipulation Algebraic Expressions

Difficulty level:  

Worksheet Overview

There are many methods for expanding double brackets.


One of them is know as FOIL.

Each letter stands for the terms we will be multiplying out:


F - First

O - Outer

I - Inner

L - Last


Remember to include the signs in front of each term when multiplying them out.


After we have multiplied each of those, we are going to simplify the expression by collecting like terms.



Let's see this in action in an example now.


e.g. Expand and simplify (x + 5)(x + 6).


First: x × x = x² 

Outer: x × +6 = +6x

Inner: +5 × x = +5x

Last: +5 × +6 = +30


Now let's simplify by collecting like terms (highlighted): 

x² + 6x + 5x + 30 = x² + 11x + 30



That wasn't so difficult, was it? 


Now it's your turn!


In this activity, you will expand and simplify two sets of brackets using the FOIL method shown above. 

You may want to have a pen and paper handy so that you can record your working. 

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