GCSE(F), GCSE(H),

**Factorising** an expression involves identifying common factors in the expression, then creating 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 3*x* + 9. The number 3 divides into both the 3 (of 3*x*) and the 9. Create a pair of brackets, and put the common factor outside the brackets, gives:

3*x* + 9 = 3(*x* + 3).

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

9*ab* + 12*b* = 3*b*(3*a* + 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: 6*x*^{2} - 2*x*:

6*x*^{2} - 2*x*

= 2(3*x*^{2} - *x*) - identifying 2 as a common factor

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

1. Factorise 4*ab* - 20*a*.

Answer: 4*a*(*b* - 5)

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

2. Factorise 15*a*^{2}*b* - 5*ab*.

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

15*a*^{2}*b* - 5*ab*

= 5(3*a*^{2}*b* - *ab*)

= 5a(3*ab* - *b*)

= 5ab(3*a* - 1)

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