A non-associative algebra (or distributive algebra) over a field K is a K-vector space A equipped with a binary multiplication operation which is K-bilinear A × A → A. Examples include Lie algebras, Jordan algebras, the octonions, and three-dimensional Euclidian space equipped with the cross product operation. Since it is not assumed that the multiplication is associative, using parentheses to indicate the order of multiplications is necessary. For example, the expressions (ab)(cd), (a(bc))d and a(b(cd)) may all yield different answers.