How to Add Polynomials by Combining Like Terms

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step tutorial on how to add polynomials by combining like terms. Hosted by Randy from MiaPrep, the lesson begins with real-world applications of polynomials, such as roller coaster design and traffic pattern analysis, before diving into the mathematical procedure. The core of the lesson focuses on identifying "like terms"—terms that share the exact same variable and exponent—and simplifying a complex expression involving two distinct polynomials. The video explores key algebraic themes including the definition of like terms, the role of variables and exponents, the conceptual understanding of constants (as terms with $x^0$), and the rules for handling parentheses during addition. It meticulously breaks down an example problem, $(2x^3 - 8x^2 - 6x + 5) + (-x^2 + 6x + 7)$, showing how to group terms and handle coefficients, including calculating sums that result in zero. For educators, this video serves as an excellent instructional tool for Algebra 1 units. It visually differentiates terms using circling techniques and addresses common stumbling blocks, such as understanding why constants can be combined or how to handle terms with no visible coefficient (like $-x^2$). The video effectively bridges abstract algebraic rules with concrete visual demonstrations, making it useful for introducing the topic or reinforcing concepts for struggling students.