Distributive Property

Theorem
Multiplication distributes over addition. That is, $$a \cdot (b + c) = a \cdot b + a \cdot c$$.

Note
In general, this name is used most often in elementary math courses. As such, it typically refers to Integer Multiplication Distributes over Addition, or on occasion Real Multiplication Distributes over Real Addition.

In other contexts, it could be applied to Complex Multiplication Distributes over Complex Addition, Multiplication Modulo m Distributes over Addition, or Matrix Multiplication Distributes over Matrix Addition, although these uses are much less frequent because these sets of numbers are not generally examined in early math courses.

Proof
See the proofs that multiplication distributes over addition for the specific sets of numbers listed in the note section.