What can you conclude about the expression (2+x)(4-2x+x²)?

To determine the validity of the conclusion regarding the expression (2+x)(4-2x+x²), it’s important to examine the form of the quadratic that emerges after expansion. When you expand (2+x)(4-2x+x²), you multiply each term in the first binomial by each term in the second, resulting in a polynomial expression.

The resulting expression can be examined for specific factoring types, such as cubes or squares. The answer states that it factors to a sum of cubes, which suggests it would take the form ( a^3 + b^3 ). However, the given polynomial does not match this specific pattern; rather, it can be recognized as a quadratic that can be rearranged or simplified through standard factoring methods.

Therefore, the correct conclusion would actually be that the expression does not fit the sum of cubes factoring method. In fact, after proper expansion and simplification, the expression does show it can be factored in a more straightforward manner. For this reason, careful analysis of polynomial forms and how they can be factored leads to the appropriate conclusions about the structure rather than settling upon sum of cubes.

In summary, proper evaluation reveals that the expression does not align with the sum of cubes, and instead,