*Factorising* an expression involves identifying common factors in the expression, then creating brackets and putting the factors outside the brackets. A common factor can be a number or a letter, or a combination of numbers and letters. It is the opposite of expanding an expression.

An example is to factorise `3x + 9`. The number 3 divides into both the 3 (of `3x`) and the 9. Create a pair of brackets, and put the common factor outside the brackets, gives:

`3x + 9 = 3(x + 3)`

Factorising `9ab + 12b` has both 3 and `b` as factors:

`9ab + 12b = 3b(3a + 4)`

because 3 divides into both 9 and 12, and `b` divides into both `ab` and `b`.

It is often easier to identify one factor at a time: `6x^2 - 2x`:

`6x^2 - 2x`

`= 2(3x^2 - x)` - identifying 2 as a common factor

`= 2x(3x - 1)` - identifying `x` as a common factor.

Factorise `4ab - 20a`

The common factors are 4 and `a`; so the two factors act as multipliers outside the bracket.

Answer: `4a(b - 5)`

Factorise `15a^2b - 5ab`

`15a^2b - 5ab`

`= 5(3a^2b - ab)`

`= 5a(3ab - b)`

`= 5ab(3a - 1)`

Answer: 5*ab*(3*a* - 1)

See also Factors

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