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Expanding Brackets GCSE Maths

Expanding brackets is one of the most important algebra skills in GCSE Maths. It appears in simplifying expressions, solving equations, and rearranging formulae, so students need to feel confident with it.

The key idea is simple: multiply everything outside the bracket by everything inside the bracket.

What Does Expanding Brackets Mean?

Expanding brackets means removing the bracket by multiplying the term outside through the expression inside.

For example:

3(x + 4)

means multiply 3 by x, and multiply 3 by 4.

So:

3(x + 4) = 3x + 12

How to Expand a Single Bracket

Example:

5(a + 2)

Step 1: Multiply 5 by a

5 × a = 5a

Step 2: Multiply 5 by 2

5 × 2 = 10

Answer:

5(a + 2) = 5a + 10

Example with Subtraction Inside the Bracket

4(x - 7)

Step 1: Multiply 4 by x

4x

Step 2: Multiply 4 by -7

-28

Answer:

4(x - 7) = 4x - 28

Example with Negatives

-3(y + 5)

Step 1: Multiply -3 by y

-3y

Step 2: Multiply -3 by 5

-15

Answer:

-3(y + 5) = -3y - 15

Expanding Two Brackets

At GCSE Higher level, students often need to expand two brackets.

Example:

(x + 2)(x + 5)

Multiply each term in the first bracket by each term in the second:

x × x = x²

x × 5 = 5x

2 × x = 2x

2 × 5 = 10

Now collect like terms:

x² + 5x + 2x + 10 = x² + 7x + 10

Common Mistakes

  • forgetting to multiply every term inside the bracket
  • sign mistakes with negative numbers
  • writing 3(x + 4) as 3x + 4 instead of 3x + 12
  • expanding correctly but forgetting to simplify like terms

Quick Practice Questions

  1. 2(x + 6)
  2. 7(a - 3)
  3. -4(y + 8)
  4. 3(2x + 5)
  5. (x + 3)(x + 4)

Answers

  1. 2x + 12
  2. 7a - 21
  3. -4y - 32
  4. 6x + 15
  5. x² + 7x + 12

Final Tip

When expanding brackets, slow down and check that every term has been multiplied properly. Most mistakes happen because one term gets missed or a negative sign is handled incorrectly.

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