In Exercises 15–58, find each product. (x−1)^3

Key Concepts

Binomial Expansion

Binomial expansion is a method used to expand expressions that are raised to a power, particularly those in the form of (a + b)^n. The expansion is achieved using the Binomial Theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n. This concept is essential for expanding polynomials like (x - 1)^3.

Cubic Functions

Cubic functions are polynomial functions of degree three, typically expressed in the form f(x) = ax^3 + bx^2 + cx + d. Understanding cubic functions is crucial for recognizing the behavior of the graph, including its turning points and intercepts. In the context of the question, expanding (x - 1)^3 results in a cubic polynomial.

Factoring and Simplifying Polynomials

Factoring and simplifying polynomials involves rewriting a polynomial as a product of its factors, which can make it easier to analyze or solve. This process often includes identifying common factors or applying special product formulas. In the case of (x - 1)^3, recognizing it as a repeated factor allows for straightforward expansion and simplification.