Expanding brackets Revision Notes for Edexcel GCSE Maths

Expanding brackets

What is expanding brackets?

Expanding brackets is the process of multiplying out brackets in algebraic expressions. This is also sometimes called multiplying out brackets. It's a fundamental skill in algebra that you'll use frequently in your GCSE maths exam.

When you encounter an expression like $4n(n + 2)$ , you need to multiply the term outside the brackets by each term inside the brackets to get the expanded form.

The golden rule

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The Golden Rule for Expanding Brackets

You must multiply the expression outside the brackets by everything inside the brackets.

For example, when you see $4n(n + 2)$ , you need to:

Multiply $4n$ by $n$ to get $4n²$
Multiply $4n$ by $2$ to get $8n$
So $4n(n + 2) = 4n² + 8n$

This rule applies to every term inside the brackets - don't miss any!

Dealing with negative signs

You need to be extra careful when there are negative signs outside the brackets. Understanding how negative signs behave is crucial for getting the right answer every time.

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Key Rules for Negative Signs:

When multiplying negative terms, it's like multiplying negative numbers
When both terms are positive or both terms are negative, the answer is positive
- Example: $-2a × -a = +2a²$
When one term is positive and one term is negative, the answer is negative
- Example: $-10p × 5q = -50pq$

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Worked Example: Expanding with Negative Signs

Expand $-2(x - y)$

Solution:

$-2 × x = -2x$
$-2 × -y = +2y$ (negative × negative = positive)

Answer: $-2x + 2y$

Notice how the negative outside the brackets changes the signs of the terms inside.

Expand and simplify

Sometimes you'll be asked to expand and simplify. This is a two-step process that requires you to be systematic and careful.

The process involves:

First: Multiply out the brackets (expand)
Second: Collect like terms together (simplify)

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Worked Example: Expand and Simplify

Expand and simplify $6(m + 2) + 4(3 - m)$

Step 1 - Expand each bracket:

$6 × m = 6m$
$6 × 2 = 12$
$4 × 3 = 12$
$4 × -m = -4m$

So we get: $6m + 12 + 12 - 4m$

Step 2 - Simplify by collecting like terms:

$m$ terms: $6m - 4m = 2m$
Number terms: $12 + 12 = 24$

Final answer: $2m + 24$

Remember that any negative signs belong to the term on their right when collecting like terms.

Worked examples

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Worked Example 1: Basic Expanding

Expand $5(2y - 3)$

Solution:

$5 × 2y = 10y$
$5 × -3 = -15$

Answer: $10y - 15$

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Worked Example 2: Expand and Simplify

Expand and simplify $2(3x + 4) - 3(4x - 5)$

Step 1 - Expand each bracket:

$2(3x + 4) = 6x + 8$
$3(4x - 5) = 12x - 15$

Step 2 - Write out the full expression: $6x + 8 - 12x + 15$

Step 3 - Collect like terms:

$x$ terms: $6x - 12x = -6x$
Number terms: $8 + 15 = 23$

Answer: $-6x + 23$

Exam tips

Here are the most important strategies to help you succeed with expanding brackets questions:

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Essential Exam Strategies:

Be careful with negative signs - this is where most mistakes happen
Always multiply the outside term by every term inside the brackets
When asked to expand and simplify, remember to collect like terms at the end
Check your signs carefully - negative × negative = positive, positive × negative = negative
Show all your working steps clearly - this can earn you partial marks even if your final answer is wrong

Summary

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Key Points to Remember:

Expanding brackets means multiplying the outside term by everything inside
The golden rule applies every time - multiply by every term inside
Negative signs need extra care - follow the multiplication rules
Expand and simplify means multiply out first, then collect like terms
Double-check your signs - this is the most common source of errors

Expanding brackets (Edexcel GCSE Maths): Revision Notes