Hello there! Today we are on factorisation, lets be together

What is Factorisation?

Factorisation means writing a mathematical expression as a product of its factors.
It is the opposite of expanding brackets.

Remember expanding brackets is the technique of removing the brackets by multiplying out the factors

Example of expansion:
3x(x+4)

= 3x(x) + 3x(4)

= 3x² + 12x

(Note: Here we have multiplied 3x by x and then the same 3x by + 4 , this is because 3x there means it is multiplying every term inside the bracket)

Factorisation does the reverse of expansion:
3x² + 12x

= 3x(x + 4)

But how?

We easily take out the Highest Common Factor (HCF) from a two-term expression (a binomial).

First – Identify the terms

Look at the expression

6x + 9

It has two terms: 6x and 9.

Secondly – Find the Highest Common Factor (HCF)

Numbers: HCF of 6 and 9 is 3.

Variables: only the first term has x, so no variable is common to both.

Thirdly – Take out the HCF

Write the HCF outside a bracket.

6x + 9

=3(2x + 3)

 (dividing 6x by 3 gives 2x, and divide 9 by 3 gives 3)

Check: expanding 3(2x+3) gives the original.

More Examples

1. Example 1
     4y+8
     HCF of 4 and 8 is 4.
     Answer: 4(y+2)

2. Example 2
    15x² + 20x

HCF of 15 and 20 is 5.
Both terms have at least one x.

therefore: the factor to take out is 5x
Answer: 5x(3x + 4).

3. Example 3
     12a²b + 18ab²
        HCF of 12 and 18 is 6.
        Common variables: one a and one b.

So the factor to take out is 6ab
Answer: 6ab(2a + 3b)

4. Negative signs
    −4x − 8

If both terms are negative, factorise the negative sign too.

the HCF here is -4
Answer: −4(x + 2)

Quick Practice

Factorise these:

a. 8x + 12

b. 14y² + 21y

c. −10p−25