**What is an Algebraic Identity?**

An algebraic identity is an algebraic equation that is true for all values of the variables occurring in it.

### Important Algebraic Identities:

(i) (x + y)^{2} = x^{2} + 2xy + y^{2}

(ii) (x – y)^{2} = x^{2} – 2xy + y^{2}

(iii) x^{2} – y^{2} = (x + y)(x – y)

(iv) (x + a)(x + b) = x^{2} + (a + b)x + ab

(v) (x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2zx

(vi) (x + y)^{3} = x^{3} + y^{3} + 3xy(x + y)

(vii) (x – y)^{3} = x^{3} – y^{3} – 3xy(x – y)

(viii) x^{3} + y^{3} + z^{3} – 3xyz = (x + y + z)(x^{2} + y^{2} + z^{2} – xy – yz– zx)

(ix) If x + y + z = 0, then x^{3} + y^{3} + z^{3} = 3xyz

(x) x^{3} + y^{3} = (x + y)(x^{2} – xy + y^{2})

(xi) x^{3} – y^{3} = (x – y)(x^{2} + xy + y^{2})