Concept

Identity

An identity is an equation that is always true. $2 = 2 5 + 3 = 5 + 3$ If an identity contains variables, it will still be true, no matter what value the variables may take. $x y^{2} - z = x = y^{2} - z$ Many identities are common or famous enough in mathematics that they have 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	$(a + b)^{2} = a^{2} + 2 a b + b^{2}$
Logarithmic Identity	$lo g_{b} (b^{m}) = m$
Polynomial Identity	$(a + b)^{2} = a^{2} + 2 a b + b^{2}$