Like terms are usually defined for variables with numerical coefficients. While the definition is sufficient to combine polynomial terms, it does not help the students to combine radical, logarithmic, or trigonometric terms. The purpose of this paper is to propose a lesson that introduces a broader definition of like terms and trialed with a group of advanced high school mathematics students of age between 15-17 years in the USA. The structure of the lesson should support not only combining non-polynomial terms but also help with solving equations and finding a combination of functions. While this paper does not attempt to introduce students to the differences between parameters and variables explicitly, the idea of differentiation between these essential algebraic entities is embedded in the processes of simplifying like terms.