# Algebraic Identities

#### 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

Identity III :
x^2 – y^2 = (x + y) (x – y)

Identity IV :
(x + a) (x + b) = x^2 + (a + b)x + ab

Identity V :
(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx

Remark :
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.

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

Identity VII :
(x – y)^3 = x^3 – y^3 – 3xy(x – y)
= 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 = a2 + 2ab + b2 .

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Algebraic identities part 1 [00:08:02]
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