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Rule

Distributive Property

Multiplying a number by the sum of two or more addends produces the same result as multiplying the number by each addend individually and then adding all the products together.

a (b \pm c) (b \pm c) a = a \cdot b \pm a \cdot c = a \cdot b \pm a \cdot c

Note that the factor outside the parentheses is multiplied, or distributed, to every term inside. The Distributive Property is used to simplify expressions with parentheses.

Since the Distributive Property is an axiom, it does not need a proof.

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