Monomials

A monomial is an algebraic expression with a single term: a real-number coefficient multiplied by one or more variables raised to whole-number exponents.

A constant is also a monomial because it can be written as a constant multiplied by a variable with an exponent of 0.

Monomials can represent real-world quantities. Suppose Liam drives from his college to his apartment at a constant speed of v kilometers per hour for t hours.

The distance covered is vt, a monomial with a coefficient of 1, and both variables have an exponent of 1. This formula applies when the speed is constant.

Not all objects move at a constant speed; some accelerate. For example, when Liam drops a ball from a tenth-floor window, the ball accelerates due to gravity. The distance the ball travels after t seconds is given by the free-fall formula: one-half gt squared, where g is the acceleration due to gravity.

With g equal to 9.8, the distance simplifies to 4.9t squared. This is also a monomial, with 4.9 as the coefficient and t having an exponent of 2.

So, monomials help represent real-world situations using simple algebraic expressions.