## The Formula: (a - b)(a² + ab + b²) = a³ - b³

This formula is known as the **difference of cubes formula**. It is a fundamental algebraic identity that helps simplify expressions and solve equations involving the difference of two cubes.

### Understanding the Formula

The formula states that the product of the difference of two terms (a - b) and the sum of the squares of the first term and the product of the two terms, plus the square of the second term (a² + ab + b²), is equal to the difference of the cubes of the two terms (a³ - b³).

### Applications

The difference of cubes formula is widely used in algebra, trigonometry, and calculus. Some common applications include:

**Factoring expressions:**It allows you to factor expressions that contain the difference of two cubes into simpler expressions.**Solving equations:**It can be used to solve equations involving the difference of two cubes.**Simplifying expressions:**It helps simplify complex expressions by reducing them to a simpler form.

### Example

Let's consider an example to illustrate the use of the difference of cubes formula.

Suppose we want to factor the expression (x³ - 8). We can recognize that this expression is in the form of (a³ - b³), where a = x and b = 2. Applying the difference of cubes formula, we get:

(x³ - 8) = (x - 2)(x² + 2x + 4)

Therefore, we have factored the expression (x³ - 8) into two simpler factors.

### Conclusion

The difference of cubes formula is a powerful tool in algebra that simplifies expressions and solves equations involving the difference of two cubes. Its applications are numerous, making it an essential formula to remember.