### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Algebraic Notation

Algebraic notation is a concise way to express mathematical ideas. In algebra, letters and symbols (a, b, c, d, …, x, y, z, α, β, etc.) represent unknown quantities.

For example, is the same as . In algebra, can be written as or simply .

is , since we have three added together.

stands for and stands for .

stands for and stands for .

Algebraic expressions can be simplified by combining like terms. Here are some examples of simplifying algebraic expressions:

Coefficients are the numbers that multiply a variable. For example, in the expression :

• 10 is the coefficient of a
• 12 is the coefficient of b
• 3 is the coefficient of ab
• 1 is the coefficient of

Fractions can also be used to represent division. For example, can be expressed as .

Let’s take a look at some more examples:

## Examples

Example 1:

Simplify the following expression:

First, group the like terms together:

Now, combine the like terms:

So, the simplified form of the expression is:

Example 2:

Simplify the expression:

Group the like terms together:

The a’s:

The ‘s:

The ab’s:

Now, combine the terms to get the simplified expression:

Note that we can also write the expression in different ways, such as:

or

or

All of these expressions are correct, as the order of the terms does not affect the overall value of the expression. Keep in mind that, in general, .

Example 3:

Simplify the following

i)

ii)

iii)

iv)

v)

i)

ii)

iii)

iv)

v)