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Concept

Identity

An identity is an equation that is always true. It may or may not contain variables. If an identity contains variables, no matter what value the variables take, the equation will always hold true.

Identity Without Variables 3 = 3 Identity With Variables (a - b) (a + b) = a^{2} - b^{2}

Many identities are so well-known and commonly used that they have their own specific names.

Name	Identity
Additive Identity	$a + 0 = a$
Multiplicative Identity	$a \cdot 1 = a$
Pythagorean Identity	$sin^{2} (θ) + cos^{2} (θ) = 1$
Square of a Binomial	$(a + b)^{2} = a^{2} + 2 a b + b^{2}$

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