What is the Expansion of (a^3- b^3)?

The expansion of (a³ – b³) is:

a³– b³ = (a – b)(a² + ab + b²)

To derive this expansion, we can use the difference of cubes formula, which states that (a³ – b³) can be factored as (a – b)(a² + ab + b²).

Here’s a brief explanation of the steps:

1. Start with the expression a³ – b³.
2. Recognize that it fits the difference of cubes pattern, where a and b are the cube roots of a³ and b³, respectively.
3. Apply the difference of cubes formula, which is (a – b)(a² + ab + b²).

So, the expansion of (a^3 – b^3) is (a – b)(a² + ab + b²). This formula is frequently used in algebraic expressions and simplifications involving cube differences.