Problem 29 of 7
Extend cube identities with complex roots for x^3+1.
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
factor and interpret complex components where applicable.
Hidden until you reveal it.
Use cube identity first, then interpret nonreal roots from the quadratic factor when needed.
Enter your answer
Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. Apply sum or difference of cubes identity.
2. Solve any quadratic factor with negative discriminant over complex numbers.
3. State real and nonreal components.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Treating the quadratic factor as having no roots over complex numbers.