1. Expanding
(brackets)

2. Rule: everything inside the brackets is multiplied by whatever is outside the brackets.
Example:
3 x X = 3X
3 (X + 4)
3 x 4 = 12
= 3X + 12

3. 5 (2X - 12) = 10X – 60 Note: care must be taken with the signs.
Example 2:
5 x 2X = 10X
5 (2X - 12)
5 x -12 = -60
= 10X – 60
Note: care must be taken with the signs.

4. 3X (2X + 4) = 6X2 + 12X Note: remember that X x X = X2. Example 3:

5. What about double brackets?
The Rule still holds, but this time you will have 4 “mini” calculations to do, and maybe some tidying up as well.
First
3X x 2X = 6X2
Last
6 x 4 = 24
(3X + 6) (2X + 4)
Outside
3X x 4 = 12X
Inside
6 x 2X = 12X
6X2 + 12X + 12X + 24
6X2 + 24X + 24 =

6. Your Turn!!! 2x(5 + x) 10x + 2x2 ½(10x + 5) 5x + 2.5 -8(3x – 2)
5x(4x + 2y)
(2x + 2)(3x + 3)
(-x + 4)(x – 7)
(9 – 3x)(4 – 2x)
(½x + ¾)(½x + 1)
3(2x + 1)(5x – 1)
(x + 4)2
10x + 2x2
5x + 2.5
-24x + 16
20x2 + 10xy
6x2 + 12x + 6
-x2 + 11x – 28
36 – 30x + 6x2
¼x2 + 7/8x + ¾
(6x+3)(5x-1)
= 30x2 +9x - 3
(x+4)(x+4)
=x2+4x+4x+16
=x2+8x+16