How do you factor x³ - 1?

Factoring the expression x³ - 1 involves recognizing it as a difference of cubes. The formula for factoring a difference of cubes is:

Difference of Cubes Formula

The general formula is:

• a³ - b³ = (a - b)(a² + ab + b²)

Applying the Formula

In the case of x³ - 1, we can identify:

• a = x
• b = 1

Now, substituting these values into the formula gives:

Factored Form

x³ - 1 = (x - 1)(x² + x + 1)

Summary

The expression x³ - 1 can be factored into (x - 1)(x² + x + 1). This shows both the linear factor and the quadratic factor that results from the difference of cubes.