1. Mutiplying Brackets

2. 2(x+2) means multiply x+2 by 2
+ 4
2 × x = 2x
2 × 2 = 4
4(x-3)
= 4x
- 12
4 × x = 4x
4 × -3 = -12
-5(x-6)
= -5x
+ 30
-5 × x = -5x
-5 × -6 = +30

3. 3(x - 4) + 2(x - 3)
= 3x
- 12
+2x
- 6
= 5x - 18
3(2x - 4) - 2(x + 5)
= 6x
- 12
-2x
- 10
= 4x - 22

4. Expand and simplify
1) 4(x + 2) 2) 5(x + 7) 3) 6(x + 8)
4) 3(3x + 4) 5) 5(6x + 1) 6) 3(5x + 2)
7) –2(x + 3) 8) –4(x + 2) 9) –6(x + 7)
10) 5(x – 7) 11) 3(x – 4) 12) 7(x – 5)
13) –5(x – 2) 14) –3(x – 3) 15) –4(x – 1)
16) –6(2x – 5) 17) –4(x – 2) 18) –2(x – 3)
19) –4(–3x + 3) 20) –7(–5x – 6)
1) 3(x + 3) + 4(x + 2) 2) 6(x + 4) – 2(x + 3)
3) 5(x + 3) + 2(x – 4) 4) 5(x + 3) + 4(x – 2)
5) 5(x – 4) + 3(x – 5) 6) 7(x – 4) – 4(x + 9)
7) 2(2x – 4) – 6(x + 3) 8) 5(3x + 6) – 4(x – 4)
9) –5(3x + 5) – 2(2x + 3) 10) 6(x + 2) – 3(3x – 5)

5. Multiplying brackets containing x terms
5×5 = 52
3 × 3 × 3 = 33
Using algebra x × x = x2
x × x × x = x3
2 × x × x = 2x2
2x × 3x =
6x2
2 × 3 = 6
x × x = x2

6. To Multiply 2 brackets use F O I L
F O I L means multiply
First by First
Outer by Outer
Inner by Inner
Last by Last
(x + 1) (x + 2) = x2
+ 2x
+ 1x
+ 2
Last by Last
Inner by Inner
First by First
Outer by Outer
= x2 + 3x +2 x2
– 3x
+ 1x
– 3
First by First
Inner by Inner
Outer by Outer
Last by Last
(x + 1) (x – 3) =
= x2 – 2x – 3
(x – 2) (x – 3) = x2
– 3x
– 2x
+ 6
= x2 – 5x + 6

7. First by First
Outer by Outer
Inner by Inner
Last by Last
(2x – 1)(x + 3) =
2x2
+ 6x
– x
– 3
= 2x2 + 5x – 3
(2x – 1)(3x – 4) =
6x2
– 8x
– 3x
+ 4
= 6x2 – 11x + 4
(2x – 1)2
means (2x – 1) (2x – 1)
(2x – 1)(2x – 1) =
4x2
– 2x
– 2x
+ 1
= 4x2 – 4x + 1

8. 1) (x + 3)(x + 2) 2) (x + 4)(x + 3) 3) (x + 3)(x – 4)