Factorising

Factorising

Factorising (put in brackets) can be said to be the 'opposite of expanding brackets'.

To factorise an expression live 3w+12 you find out the highest factor the terms have in common.
In this case it is 3. That means 3 needs to be outside the bracket.
Then you find out what you multiply by 3 to get 3w and what you multiply by 3 to get 12.

3 x w = 3w and 3 x 4 = 13 since 3 is the highest factor both terms have in common.

so factorising 3x+12 gives 3(w+4).

Examples:

Factorise the following expressions

1) 4y + 12
The highest common factor is 4, so 4 has to be outside the bracket.
4 x y = 4y and 4 x 3 = 12

so 4y + 12 = 4(y + 3)

2) 30b + 42
The highest common factor is 6, so 6 has to be outside the bracket.
6 x 5b = 30b and 6 x 7 = 42

so 30b + 42 = 6(5b + 7)

3) 6v + 15w
The highest common factor is 3, so 3 has to be outside the bracket.
3 x 2v = 6v and 3 x 5w = 15w

s0 6v + 15w = 3(2v + 3w)