What is a trinomial square?

When a binomial algebraic expression is squared, the result is a trinomial square. If (a + b) is squared, it yields a trinomial square. The expression (a + b) is a binomial and not a trinomial.

A binomial has two algebraic expressions, while a trinomial has three algebraic expressions.

(a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b² are both the squares of a binomial. The expressions a² + 2ab + b² and a² - 2ab + b² are both trinomial squares. These algebraic expressions are also referred to as expansion formulas or identities in algebra.