2. Algebra

Expanding Brackets

What are brackets in Maths?

Brackets are used in mathematics to group terms together, making expressions and calculations easier to understand and solve. They also help us decide on the order of operations.

For example: $(3 + 2) \times (- 7)$ or $5 (2 x + 3)$ or $(7 - 2 x) (3 x + 8)$

What does expanding brackets mean?

When brackets are next to each other or have a number outside them that means we need to multiply the two things together, this is called expanding brackets. It is the opposite of factorising where we put brackets back into an expression.

For example: $5 (2 x + 3)$ means $5 \times (2 x + 3) = 10 x + 15$

Why do we need to expand brackets?

Expanding brackets is a crucial skill in algebra, as it helps simplify expressions and solve equations more efficiently. By expanding brackets, we can then combine like terms, making expressions easier to understand and simpler to work with. This skill is vital for success in your exam. It also forms the foundation for more advanced algebraic techniques you'll encounter later in your maths course.

Expanding Single Brackets

Expanding single brackets involves multiplying each term inside the bracket by the term outside the bracket.

Example: Expand the expression $3 (x + 4)$ .

$3 \times x = 3 x 3 \times 4 = 12 3 (x + 4) = 3 x + 12$

Here, we multiplied each term inside the bracket $x$ and $4$ by the term outside the bracket $3$ .

Exam Tip: Beware of minus signs

Remember the basic rules of multiplication with signs
- $- \times - = +$
- $- \times + = -$
It helps to put brackets around negative terms

Expanding Double Brackets

Expanding double brackets involves multiplying two expressions enclosed in brackets. There are lots of different methods to expand brackets, using grids, lines or FOIL.

The FOIL method is a popular technique used to expand double brackets, where FOIL stands for First, Outer, Inner and Last. This helps to systematically work through multiplying each part within the one bracket with each part in the other.

Example: Expand the expression $(x + 3) (x - 2)$ .

Using the FOIL method:

First: $x \times x = x^{2}$

Outer: $x \times - 2 = - 2 x$

Inner: $3 \times x = 3 x$

Last: $3 \times - 2 = - 6$

Writing all the terms out together

$x^{2} - 2 x + 3 x - 6$

Finally, we can simplify by collecting like terms

$x^{2} + x - 6$

Expanding Brackets with Powers

When expanding brackets raised to a power, this just means the entire bracket multiplied by itself that many times.

Example: Expand the expression ${(x + 2)}^{2}$ .

First, write the expression out fully

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

Now, apply the FOIL method:

First: $x \times x = x^{2}$

Outer: $x \times 2 = 2 x$

Inner: $2 \times x = 2 x$

Last: $2 \times 2 = 4$

Combining the terms, we get: $x^{2} + 2 x + 2 x + 4$ , which simplifies to $x^{2} + 4 x + 4$ .

Expanding Brackets: Practice and Revision Tips

To excel in expanding brackets questions in your exam, practice and revision are essential. Here are some tips to help you master this crucial skill:

Practise different types of questions: Make sure you practise a variety of expanding brackets problems, including single brackets, double brackets, and brackets with exponents. This will help you become comfortable with different scenarios and boost your confidence.

Check your answers: As you work through practice problems, ensure you check your answers by factoring your expanded expressions back into brackets. This will help you confirm that you have expanded the brackets correctly.

Use revision resources: Utilise various revision resources, such as online videos, revision guides, and past exam papers, to reinforce your understanding of expanding brackets. Save My Exams offers a wealth of resources, including topic-specific revision notes, to help you prepare for your exams.

Create flashcards: Flashcards are a great way to memorise key concepts and techniques related to expanding brackets. Write down important rules, examples, and steps for expanding different types of brackets, and review them regularly.

Examiner's tip: Expanding Brackets

Expanding brackets is an essential skill for success in your exams. By understanding the concept, practising different types of problems, and using our revision tips, you'll be well-prepared to tackle any expanding brackets question with confidence. Remember, practice makes perfect - so keep working on those brackets, and you'll soon become an expert in expanding them!

Edexcel GCSE Maths

Revision Notes