#### notes

An algebraic identity is an algebraic equation that is true for all values of the variables occurring in it. **Identity I :** `(x + y)^2 = x^2 + 2xy + y^2 `**Identity II :** `(x – y)^2 = x^2 – 2xy + y^2`

**`x^2 – y^2 = (x + y) (x – y)`**

Identity III :

Identity III :

**`(x + a) (x + b) = x^2 + (a + b)x + ab`**

Identity IV :

Identity IV :

**`(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx`**

Identity V :

Identity V :

**We call the right hand side expression the expanded form of the left hand side expression. Note that the expansion of `(x + y + z)^2` consists of three square terms and three product terms.**

Remark :

Remark :

**Identity VI :**` (x + y)^3 = x^3 + y^3 + 3xy (x + y)`

**`(x – y)^3 = x^3 – y^3 – 3xy(x – y) `**

Identity VII :

Identity VII :

= `x^3 – 3x^2y + 3xy^2 – y^3`

**Identity VIII :** `x^3 + y^3 + z^3 – 3xyz = (x + y + z)(x^2 + y^2 + z^2 – xy – yz – zx)`

#### description

( a + b )^{2} = a^{2} + 2ab + b^{2} .