# Algebraic Identities

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An equality which is true only for certain values of variables in it, is called an equation.

An identity is an equality, which is true for all values of the variables in the equality. On the other hand, an equation which is true only for certain values of its variables, is not an identity.

Algebraic identity is defined as an algebraic relation of equality that remains true for all values of variables occurring in the relation.

Square Identities:

Square of sum of two terms: (a + b)2 = a2 + 2ab + b2

Square of difference of two terms: (a – b)2 = a2 – 2ab + b2

Product of sum and difference of two terms: (a + b)(a – b) = a2 – b2

Square of a trinomial: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

(x + a)(x + b) = x2 + (a + b)x + ab

Cube Identities:

Cube of sum of two terms: (a + b)3 = a3 + b3 + 3ab (a + b)

Cube of difference of two terms: (a – b)3 = a3 – b3 – 3ab (a – b)

Using above identities, following identities can be proved:

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