Identity: GCSE Maths Definition

What is an identity?

In GCSE maths an identity is a mathematical statement that shows that two expressions are equal for all values of the variables involved. It is written with an identity sign () between two expressions which are always equal, no matter what values are substituted in for the variables.

Unlike a formula or equation, which may only apply to particular situations or if certain conditions are satisfied, an identity is always true in all possible circumstances.

An identity cannot be solved. Instead it has the purpose of showing two expressions are equal in all cases, and it is generally used to simplify expressions. For example, means is identical to for every value of .

Some identities you will be likely to use in GCSE maths are:

• Algebraic identities such as the difference of two squares: ; or a perfect square:

• Identities in Powers Rules such as the product of powers rule: ; the power of a power rule: ; or the negative power rule:

At GCSE level you may often find you are using identities without realising it, and it is okay in the examples above to replace the identity sign with an equals sign when using them.

Identities revision resources to ace your exams

You can find out more about identities, and how they can be used, by reading our revision notes. To test your knowledge, try our exam questions in the algebra section.

For quick-fire GCSE maths revision, use our collection of interactive flashcards for GCSE maths. We also have past papers for your exam practice.

Explore our GCSE maths revision resources