Distributive Property

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Theorem

Multiplication distributes over addition.

That is:

$a \cdot \left({b + c}\right) = a \cdot b + a \cdot c$

where $a, b, c$ are numbers.


Proof

See Multiplication of Numbers Distributes over Addition.


$\blacksquare$


Note

In general, this name is used most often in elementary mathematics courses to mean Multiplication of Numbers Distributes over Addition.

As such, it typically refers to:

In other contexts, it could be applied to:

although these uses are much less frequent because these sets of numbers are not generally examined in early mathematics courses.

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