- What is an Identity
An identity is an equation that is true for all values of the variables. For example:
`(x + y)^2 = x^2 + 2xy + y^2`
The above equation is true for all possible values of x and y, so it is called an identity.
An identity is true for any value of the variable, but an equation is not. For example the equation
3x = 12
is true only when x=4, so it is an equation, but not an identity. In fact, when we see an equation like that, we are usually trying to solve it. That is, find the single value of x that makes the equation true.