Which factorization applies to the difference of cubes?

The factorization that applies to the difference of cubes is given by the expression where A represents a perfect cube minus another perfect cube, B. Specifically, the formula states that A³ - B³ can be factored into the product of a binomial and a trinomial as follows:

A³ - B³ = (A - B)(A² + AB + B²)

In this factorization, the first part, (A - B), indicates the difference of the two cubes, while the second part, (A² + AB + B²), expands to produce the original difference of cubes when multiplied out. This trinomial includes the square of the first term, the product of the two terms, and the square of the second term, showcasing how all components contribute to the initial expression.

This factorization is crucial because it allows for the simplification of algebraic expressions involving cubic terms and provides a method for solving equations that include cubic polynomials. Understanding and using this factorization is essential in algebra, particularly in higher-level math courses where cube equations frequently occur.