# Distributive Property

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## Distributive Property

(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)nan + bn.

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The distributive property can be equally well shown with an array (see Figure 4).
This model can also be used to demonstrate that it does not matter how the numbers are partitioned--we use ten because it makes the calculations easier, but the distributive property is not restricted to partitions involving tens (Figure 7).

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