1. The problem is to expand the expression $a^3 + b^3$. 2. We use the sum of cubes formula: $$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$. 3. This formula states that the sum of two cubes can be factored into a product of a binomial $(a+b)$ and a trinomial $(a^2 - ab + b^2)$. 4. Applying the formula directly, the expanded form of $a^3 + b^3$ is: $$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$ 5. This is the fully factored form; if you want to expand it back, you multiply: $$(a + b)(a^2 - ab + b^2) = a^3 - a^2b + ab^2 + a^2b - ab^2 + b^3 = a^3 + b^3$$ 6. Notice the middle terms cancel out, confirming the factorization is correct. Final answer: $$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$