To factorise expressions we 'take out' (if possible) the highest common factor (HCF), which is the biggest number that divides exactly by each term in the expression.

For example, the HCF between 5 and 20 is 5. The HCF between 6 and 9 is 3. The HCF between 4x and 10x is 2x.

When factorising expressions we divide the whole expression by the HCF, we then leave this inside brackets, and take the HCF outside the brackets. So that when you multiply together the HCF on the outside, by the expression on the inside, you end up with what you started with.

Example 1

Factorise 8x-56

8x-56 is the expression.

The HCF of this expression is 8. No matter what x is, '8x' divides by 8 and 8 goes into the '56' 7 times.

We now divide our expression by 8 which gives us (x-7)

So we leave 8 on the outside of the bracklet and (x-7) inside. 

So we get

8(x-7) = 8x - 57

Example 2

Factorise 2x2-12x

If we are looking at common factors that are just numbers, we can clearly see that 2 would be the HCF. But both terms (2x2 and 12x) both have at least 1 x term. Remember that x is still a number, we just don't know what it is. So the HCF is 2x. 

We divide 2x2 by 2x which gives us x.

We divide 12x by 2x which gives us 6.

So, we get 2x on the outside of the bracket, and x - 6 on the inside of the bracket giving us:

2x2-12x = 2x(x-6)

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AQA Unit 2 November 2012 (H) - Page 7, Question 9 

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