The algebraic identity
Letting
and 
gives Lagrange's identity.
The n = 2 case gives
The n = 3 case is equivalent to the vector identity
where
is the dot product and 
is the cross product. Note that this identity itself is sometimes known as Lagrange's identity.
(1)
Letting
and gives Lagrange's identity. The n = 2 case gives
(2)
The n = 3 case is equivalent to the vector identity
(3)
where
is the dot product and is the cross product. Note that this identity itself is sometimes known as Lagrange's identity. 
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