Ever wondered how to pack things back into their boxes?

Aisha has 12x biscuits and 18 sweets to share into identical party packs for her brother's birthday. Using 6 packs, each gets 2x biscuits and 3 sweets: 12x + 18 = 6(2x + 3). Writing it that way is called factorising.

Revision notes

📒 Factorising Simple Expressions: lesson notes

Put brackets back in: find the highest common factor of the terms and take it outside.

Expanding backwards

We know 6(2x + 3) = 12x + 18. Factorising goes the other way: from 12x + 18 back to 6(2x + 3).

Find the highest common factor (HCF) of the terms. For 12x and 18, the HCF is 6.

Put the HCF outside the bracket, and divide each term by it: 12x ÷ 6 = 2x and 18 ÷ 6 = 3. So 12x + 18 = 6(2x + 3).

🔑 Key idea: Factorising is the reverse of expanding: take out the HCF.

Letters can be common factors too

In 6x² + 9x, both terms contain 3 AND x, so the HCF is 3x.

6x² ÷ 3x = 2x and 9x ÷ 3x = 3, so 6x² + 9x = 3x(2x + 3).

Always check by expanding: 3x × 2x + 3x × 3 = 6x² + 9x ✓. If something common is still left inside the bracket, you haven't finished.

🔑 Key idea: Factorise completely: take out the HIGHEST common factor, then check by expanding.

Worked example

Factorise completely: 12x + 15

Step 1: Find the HCF of the terms
HCF of 12 and 15 = 3
Step 2: Divide each term by the HCF
12x ÷ 3 = 4x
15 ÷ 3 = 5
12x + 15 = 3(4x + 5)
Step 3: Check by expanding
3(4x + 5) = 12x + 15 ✓
Why? Factorising is the reverse of expanding.

Answer: 3(4x + 5)

Summary

Factorising puts brackets back in — it is the reverse of expanding.
Find the HCF of all the terms (numbers and letters) and put it outside.
Divide every term by the HCF to fill the bracket.
Check your answer by expanding it.