Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which formula represents the sum of cubes?

1. (a+b)(a²-ab+b²)

2. (a-b)(a²+ab+b²)

3. (y₂-y₁)/(x₂-x₁)

4. a²+2ab+b²

The correct answer is: (a+b)(a²-ab+b²)

The sum of cubes is represented by the formula \(a^3 + b^3 = (a+b)(a^2 - ab + b^2)\). This formula is derived from the fact that when you multiply the binomial \((a+b)\) by the trinomial \((a^2 - ab + b^2)\), the result is indeed \(a^3 + b^3\), demonstrating how the two expressions are interconnected. In this case, recognizing that the question asks for the representation of the sum of cubes confirms the correctness of the choice linked to the formula provided. The other options either represent different algebraic identities or do not relate to the concept of the sum of cubes at all. For example, a difference of cubes or quadratic expressions might appear in those choices, but they do not align with the specific formulation pertaining to the sum of cubes.