Distributive Property

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(distributive law), the property of multiplication expressed by the identities c(a + b) = ca + cb and (a + b)c = ac + be. In a more general sense, the distributive property of the operator F(x) with respect to some operation x * y is referred to as a property expressed by the equality F(x *y) = F(x) * F(y). For example, the equality (ab)ⁿ = aⁿbⁿ shows that the operator of involution is distributive with respect to the operation of multiplication but not with respect to the operation of addition, since, generally speaking, (a + b)ⁿ ≠ aⁿ + bⁿ.

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