Polynomial expansions involve expressing a polynomial as a sum of its terms, which are made up of variables raised to whole number powers and multiplied by coefficients. For example, the polynomial 2x^2 + 3x + 5 consists of three terms: 2x^2, 3x, and 5. This representation helps in understanding the behavior of the polynomial, such as its roots and graph. One common method of polynomial expansion is the binomial theorem, which provides a formula for expanding expressions of the form (a + b)^n. This theorem allows for quick calculations of coefficients in the expansion, making it easier to work with polynomials in algebra and calculus.