Distributive property

A law stating that one operation applied to a combined expression can be computed by applying it to each part and combining the results. Multiplication distributes over addition and subtraction.

Multiplication over addition: The rule a(b + c) = ab + ac for numbers and algebraic expressions. This is the standard form of the distributive property.
Addition: The arithmetic operation of combining quantities into a sum. Distribution acts on sums by separating their addends.
Mental arithmetic: Calculation performed without written or electronic aids. Breaking numbers into sums makes products easier to calculate mentally.
Associative property: A law stating that regrouping operands does not change the result of an operation. Associativity changes grouping within one operation; distribution relates two operations.
Factoring: Rewriting a sum or difference as a product of simpler expressions. Factoring reverses distribution by extracting a shared factor.
Multiplication: The arithmetic operation of scaling one quantity by another. The distributing operation in the standard arithmetic law.
Expanding (algebra): Rewriting a product of sums as a sum of terms by applying algebraic laws. Expansion applies distribution repeatedly to remove grouped products.
Commutative property: A law stating that swapping the operands of an operation does not change its result. Commutativity changes operand order, which distribution does not assert.
Boolean algebra: An algebraic system for logical values and operations such as conjunction, disjunction, and negation. Its two distributive laws show that distribution is not limited to ordinary arithmetic.
Parentheses in mathematics: Grouping symbols that indicate which parts of an expression belong together. Parentheses mark the sum or difference that distribution expands.

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