1. Factorisation.
ab + ad = a( b +……..

2. Multiplying Out Brackets reminder.
Multiply out the brackets below:
(1) 6 ( x + 3 ) = 6x + 18
(2) 3 ( 2x + 5 ) = 6x + 15
(3) 4 ( 6x + 7 ) =
24x + 28
(4) 9 ( 3x + 9 ) =
27x + 81 =
(5) 2 ( 3x + 4 ) 6x + 8
(6) 8 ( 5x + 7 ) =
40x + 56

3. Putting The Brackets Back In.
In maths it is not only important to be able to multiply out brackets but also to be able to put the brackets back. This process is called FACTORISATION.
How to factorise:
Consider the expression below :
6a + 12
Can you think of a number that divides into both 6 and 12 ?
= 6 ( a +
2 )
6 is a common factor.
Now the expression is factorised.
Now take 6 outside the bracket and work out what goes inside the bracket.

4. Further Examples. Now factorise the following expressions:
5 ( x +
2 )
(2) 7 x + 21 =
7 ( x +
3 )
(3) 6 x - 9 =
3 (
2 x -
3 )
(4) 15 x - 20 =
5 (
3 x -
4 )
(5) 24 x + 8 =
8 (
3 x +
1 )

5. What Goes In The Box ? (1) 6x + 12 = 6 ( x + 2 ) (2) 9x - 18 = 9 ( x -
Factorise the following expressions:
(1) 6x + 12 = 6
( x +
2 )
(2) 9x - 18 = 9
( x -
2 )
(3) 8x + 12 = 4
( 2x +
3 )
(4) 7x - 21 = 7
( x -
3 )
(5) 10x + 15 = 5
( 2x +
3 )

6. Multiplying Out Brackets Reminder 2
Multiply out the brackets below:
(1) 3t ( 2t + 6 ) =
6t 2 +
18t
28w
(2) 4w ( 3w - 7 ) =
12w 2 -
(3) 5a ( 2a + 9 ) =
10a 2 +
45a
(4) 2z ( 5z - 8 ) =
10z 2 -
16z

7. Harder Factorisation. Factorise : 3ab – 12ad = 3 ( ab – 4 ad ) = 3a
In the example below there is more than one term to be removed from the bracket.
Factorise :
3ab – 12ad
Remove any numbers first.
= 3
( ab – 4
ad )
Now remove any letters.
= 3a
( b –
4d )
The expression is now fully factorised.

8. Further Examples. Factorise the following expressions: (1) 5wg – 10 wm
(3) 9ab + 12bc
= 5 ( wg –
wm )
= 3 (
3ab +
4bc )
= 5w
( g
m ) –
= 3b
( 3a +
4c )
(2) 16xy – 8xw
(4) 6x2 + 9 xy
= 8 (
2xy –
xw )
= 3 (
2x2 +
3xy )
= 8x
( 2y
w ) –
= 3x
( 2x +
3y )

9. What Goes In The Box ? (1) 6ag – 18 af (2) 7x2w + 28xy + - 3 af ) = 7
Factorise the following expressions:
(1) 6ag – 18 af
(2) 7x2w + 28xy + -
3 af )
= 7
(x2w
4 xy )
= 6
( ag -
= 7x
( xw +
4y )
= 6a
( g
3 f )