algebra.jpgIn 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.



  • An algebraic term can be made up of coefficient, variables and exponents.
  • Like terms have the same variables and exponents.

e.g. { 2a, 4a, -6a } are like terms.
a is common to all.


{ x, 3a2, 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.





4a + 6a

4a + 6a = 10a

-2x − 3x -2x − 3x = -5x

12pq − 6pq + 4pq

12pq − 6pq + 4pq = 10pq

3c + 4d2 + 5c

3c + 4d2 + 5c = 3c + 5c + 4d2

= 8c + 4d2

4x2 + 10x2 4x2 + 10x2 = 14x2




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.



3 is added to x

x + 3

5 is subtracted from y

y − 5

z is multiplied by 4


w is divided by 10
The product of x and y
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