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- What is an Identity

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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.