produktterm

Produktterm, in mathematics and statistics, refers to a term that is formed as a product of factors, typically a coefficient and one or more variables. In many algebraic contexts a term is a monomial, which means it can be written as a product of a numeric coefficient and variables raised to nonnegative integer powers. For example, 3x^2y and -7xy^3 are product terms. A constant, such as 5, is also considered a degenerate product term (a product of a single factor).

In polynomials, each summand is a term, and product terms are the basic building blocks of those summands. The degree of a product term equals the sum of the exponents of its variable factors. Terms with the same variable part are called like terms and can be combined if they have the same variable structure, though their coefficients may differ. When simplifying expressions, a common goal is to collect like terms and reduce the expression to a standard form.

In statistics, a related concept is the product term or interaction term, which represents the interaction between two or more predictor variables. Such terms are created by multiplying variables together (for example, x1*x2) to model effects that are not additive. Including product terms allows regression models to capture more complex relationships between variables.

Terminology can vary by language and field. In some contexts, a product term is essentially a monomial, while in others it specifically denotes an interaction or multiplicative combination of factors within a model.

See also: polynomial, monomial, interaction term.