Difference Cubes 4721Bc

1. **State the problem:** We need to find the factorization of the expression $$a^3 - b^3$$. 2. **Formula used:** The difference of cubes formula is: $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ 3. **Explanation:** This formula states that the difference between two cubes can be factored into a product of a binomial and a trinomial. 4. **Intermediate work:** - Identify the terms: $a^3$ and $b^3$. - Apply the formula directly: $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ 5. **Final answer:** $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ This factorization is useful for simplifying expressions and solving equations involving cubes.