In algebra, letters are used to stand for numbers.
The letters are often called variables.
It is necessary to be able to add, subtract, multiply and divide algebraic terms.
Definitions


 Like terms have the same variables and exponents.

e.g. { 2a, 4a, 6a } are like terms. a is common to all.
{ x, 3a^{2}, 6 } are unlike terms. There is no common term.

 An algebraic expression is a group of terms.

e.g. 4x + 3y is an expression.

Addition and Subtraction
An expression involving addition and subtraction can be simplified only if it contains like terms.
The like terms are collected together and then added or subtracted.
Examples 
Answers 
Simplify:

4a + 6a

4a + 6a = 10a

2x − 3x 
2x − 3x = 5x 
12pq − 6pq + 4pq

12pq − 6pq + 4pq = 10pq

3c + 4d^{2} + 5c

3c + 4d^{2} + 5c = 3c + 5c + 4d^{2}
= 8c + 4d^{2}

4x^{2} + 10x^{2} 
4x^{2} + 10x^{2} = 14x^{2} 
Multiplying
3xy means "3 multiplied by x multiplied by y ".
In terms of this type the number comes first and the variables are usually placed in alphabetical order.
e.g. 3q × 4p = 12pq
Note that numbers are multiplied first and letters (variables) are placed in alphabetical order.
Words into Symbols
Many maths problems are written in words and these words often have to be changed into algebraic expressions.
Words 
Algebra 
3 is added to x

x + 3

5 is subtracted from y

y − 5

z is multiplied by 4

4z

w is divided by 10 
^{w}⁄_{10}

The product of x and y 
xy

The difference between a and 5 
a − 5

The sum of 7 and w

7 + w

p is muliplied by q and 5 is added 
pq + 5

6 multipied by c is equal to 30 
6c = 30

