Expanding and Factorising – GCSE Maths Boost

These are basically opposites.

Expanding: take brackets away
Factorising: put brackets back

Expanding

If you have: $3(x+4)$

The 3 multiplies everything inside the bracket: $3\times x + 3\times4$

So:

$\boxed{3x+12}$

Factorising

Factorising is the opposite of expanding.

For example:

$6x+12$

Ask: What number goes into both terms?

Both 6 and 12 can be divided by 6.

Take the 6 outside a bracket:

$6(x+2)$

So:

$\boxed{6x+12=6(x+2)}$

Think of it like this:

Expanding:

$6(x+2) \rightarrow 6x+12$

Factorising:

$6x+12 \rightarrow 6(x+2)$

They’re doing the opposite thing.

GCSE tip

When factorising, look for the highest common factor (HCF).

Example:

$8x+20$

The biggest number that goes into both 8 and 20 is 4.

So:

$8x+20=4(2x+5)$

$4(2x+5)=8x+20$

The main things to remember

Skill	What you do
Expand	Multiply into the bracket
Factorise	Find the common factor and put it outside
Negative	Keep track of the signs
Check	Expand your answer back out

Shortcut:
👉 Expand = brackets disappear
👉 Factorise = brackets appear

Expanding and Factorising

1 / 10

(a) Factorise fully 30x³+12x

(b) Solve 5(f-2)=22
f =

2 / 10

(a) Expand a(a+b)

(b) Factorise 15y-6

3 / 10

(a) Factorise fully 7xy+21x

(b) Solve 6(p+3)=42
p =

4 / 10

(a) Expand 7(2h-3)

(b) Expand and Simplify 4(g+5)+3(g-2)

5 / 10

(a) Factorise x²-9x

(b) Expand 6(5y+1)

6 / 10

(a) Factorise fully 6x²-4xy

(b) Solve 2(w-4)=13
w =

7 / 10

(a) Factorise 18x+24

(b) Expand 3(2y-4)

8 / 10

(a) Factorise fully 5a²b+15ab²

(b) Solve 6(c-8)=42
c =

9 / 10

(a) Factorise fully 30a²+40ab

(b) Solve 3(g+9)=21
g =

10 / 10

(a) Factorise fully 18a²bc+30abc²

(b) Expand and Simplify 4(2y-7)-3(5y-3)

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