1. Algebraic Expressions
Algebraic Terms
Examples 2a
means
2  a
If p = 3, q = 4, r = 6 ab
means
a  b 5p
= 5  3
= 15 a2
means
a  a qr
= 4  6
= 24 a3
means
a  a  a r2
= 6  6
= 36 a b
means
a  b p3
= 3  3  3
= 27
a2b c pq r
3  4 6 = 12 6 =
means
a  a  b  c
= 2
r – p q
6 – 3 4 = 3 4 =

2. Adding and subtracting terms
Examples
5x – 4y + 2x + 6y
= 7x
+ 2y
5x x
– 4y y
2x2 – x x2 – 4x – 3
= 3x2
– 5x
+ 4
2x x2
– x – 4x
– 3
a2 + 3ab – 4b2 + 2a2 – 5ab – 7b2
= 3a2
– 2ab
– 11b2
a a2
+ 3ab – 5ab
– 4b – 7b2

3. Expanding a bracket
Examples
3(2x + 1)
= 6x
+ 3
3  2x
3  1
a(a – b)
= a2
– ab
a  a
a  – b
4p(3p + 2q – 5)
= 12p2
+ 8pq
– 20p
4p  3p
4p  2q
4p  – 5

4. Expanding 2 brackets
Examples
(2x – 3) (4x + 5)
= 8x2
+ 10x
– 12x
– 15
= 8x2 – 2x – 15
2x  4x
2x  5
– 3  4x
– 3  5
+ 10x – 12x
5(x – 2y) – 2(2x – 3y)
= 5x
– 10y
– 4x
+ 6y
= x
– 4y
5  x
5  – 2y
– 2  2 x
– 2  – 3y
5x – 4x
– 10y y
4x(x + y) + 3x(x – y)
= 4x2
+ 4xy
+ 3x2
– 3xy
= 7x2
+ xy
4x  x
3x  – y
4x x2
+ 4xy – 3xy
4x  y
3x  x
(5a – b) (2a – 3b)
= 10a2
– 15ab
– 2ab
+ 3b2
= 10a2 – 17ab + 3b2
5a  2a
5a  – 3b
– b  – 3b
– b  2a
– 15ab – 2ab

5. Perimeter and Area
Perimeter of a shape is the total length of its sides.
Perimeter of a rectangle
= length + width + length + width
length l
P = l + w + l + w
width w
width w
P = 2l + 2w
P = 2(l + w)
length l
Area of rectangle = length  width
A = lw

6. Examples 3x 2x
Perimeter
= 3x + 2x + 3x + 2x
= 10x
Area
= 3x  2x
= 6x2 4a 2b
Perimeter
= 4a + 2b + 4a + 2b
= 8a
+ 4b
Area
= 4a  2b
= 8ab
x + 5
x – 1
Perimeter
= x x – 1 + x x – 1
= 4x
+ 8
Area
= (x + 5)(x – 1)
= x2
– x
+ 5x
– 5
= x2 + 4x – 5

7. Examples Perimeter = 4x + 3y + x + 2y + 3x + 5y x = 8x + 10y A B
Area of A
= 4x  3y
= 12xy
Area of B
= 3x  2y
= 6xy
Total area =
12xy + 6xy
= 18xy