1. Multiplying Out Single Brackets.
5 X ( 2X + & )
= 10 X ………

2. What Does Multiplying Out A Bracket Mean ?
Consider this rectangle broken into two areas as shown: 6 A1 A2
We are going to work out the area of this rectangle : x 2
Area = length  breadth 6x
+ 12
A1 = 6  x
= 6x
Total Area =
A2 = 6  2
= 12

3. 6 ( x + 2 ) = 6x + 12 Now consider the expression below: Golden Rule:
Everything inside the bracket
must be multiplied by the
Number or term outside the bracket.
6 ( x + 2 ) = 6x + 12
The same as the area of the rectangle.
Now multiply out the following brackets:
(1) 4 ( x + 6 )
(2) 7 ( 2 x + 5 )
(3) 5 ( 8x + 9 )
= 4x
+ 24 =
14x
+35 =
40x
+ 45

4. What Goes In The Box 1? (1) 6 ( x + 3 ) = 6x + 18 (2) 3 ( 2x + 5 ) =
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

5. Some Algebra Revision.
You should know the answer to the following questions:
Multiply out :
Calculate :
(1) 2y  5 y =
10y 2
(1) 3  - 4 =
-12
(2) 3w  4 w =
12w 2
(2) 6  - 7 =
- 42
(3) 6r  7r =
42r 2
(3) - 3  8 =
- 24
(4) 4f  3f =
12f 2
(4) 7  - 6 =
- 42
(5) 9h  8h =
72h 2
(5) - 8  2 =
- 16

6. Harder Single Brackets.
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. What Goes In The Box 2 ? (1) 3x ( 4x – 7 ) = – (2) 6w ( 8w + 3 ) = +
(3) 2f ( 3f - 5 ) =
6f 2 –
10f
(4) 8r ( 6r + 3 ) =
48r 2 +
24r
(5) 3d ( 5d - 9 ) =
15d 2 –
27d
(6) 8a ( 9a + 3 ) =
172a2 +
24a

8. More Than One Bracket. Consider the brackets below:
Multiply out both brackets:
2( 3x + 6 ) + 2 ( 4x + 3 )
Gather like terms together.
= 6x x + 6
= 6x + 8x
Simplify by adding like terms.
= 14x + 18
You have now multiplied out the brackets and simplified the expression.

9. Multiply out the brackets below and simplify :
4 ( 3x – 5 ) + 2 ( 3x – 7 )
Solution.
4 ( 3x – 5 ) + 2 ( 3x – 7 )
= 12x – x – 14
= 12x + 6x – 20 – 14
= 18x – 34

10. Multiply out the brackets below and simplify :
4 ( 2 b + 5 ) – 6 ( 3b – 4 )
Solution
4 ( 2 b + 5 ) – 6 ( 3b – 4 )
= 8b + 20 – 18b + 24
Remember that a negative times a negative makes a positive.
= 8b – 18 b
= – 10 b + 44

11. What Goes In The Box 3 ? Multiply out and simplify the brackets below:
(1) 2 ( x + 4 ) + 3 ( x + 5)
(5) 2 ( 3g – 4 ) + 2 ( 4g – 6 )
= 5x +23
= 14g -20
(2) 3 ( 2a + 5 ) + 4 ( 3a + 3 )
(6) 5 ( 3f – 6 ) – 4( 2 f – 6 )
= 7f – 6
= 18a + 27
(7) 3 ( 4t – 6 ) – 7 ( 6t – 8)
( 3) 4 ( 5b + 2 ) + 3 ( 2b + 7)
= 26b + 29
= - 30t + 38