Multiplication and Division of Monomials - Vocabulary

Vocabulary flashcards covering key terms from the notes on monomials, exponents, and special products.

Monomial

A single term formed by a numerical coefficient multiplied by one or more variables with nonnegative integer exponents.

Numerical coefficient

The numeric multiplier of the variables in an algebraic term.

Literal coefficient

The variable part of an algebraic term, including its exponent.

Base

The number or variable that is raised to a power (the factor being multiplied repeatedly).

Exponent

The exponent; the number of times the base is multiplied in a power.

Power

A notation representing the repeated multiplication of the same factor.

Quotient of powers

When bases are the same, x^m / x^n = x^{m-n} (requires the same base).

Negative exponent

Rule: x^(-k) = 1/x^k (a negative exponent indicates reciprocal of the positive power).

Product rule (powers)

When multiplying like bases x^m · x^n = x^{m+n} (bases must be the same).

Binomial

An algebraic expression with two terms, such as a + b.

Cube of a binomial

Raising a binomial to the third power: (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3; (a−b)^3 = a^3 − 3a^2b − 3ab^2 − b^3.