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:
- Start with the expression a3 – b3.
- Recognize that it fits the difference of cubes pattern, where a and b are the cube roots of a3 and b3, respectively.
- 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.