Explation ch alegbra
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Algebraic Identities
An algebraic identity is an equality that holds for any values of its variables.
For example, the identity
(x+y)^2 = x^2 + 2xy + y^2
(x+y)
2
=x
2
+2xy+y
2
holds for all values of xx and yy.
Since an identity holds for all values of its variables, it is possible to substitute instances of one side of the equality with the other side of the equality. For example, because of the identity above, we can replace any instance of (x+y)^2(x+y)
2
with x^2 + 2xy + y^2x
2
+2xy+y
2
and vice versa.
Clever use of identities offers shortcuts to many problems by making the algebra easier to manipulate. Below are lists of some common algebraic identities
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