Final answer:
The factors of 24x⁶ - 1029y³ are 3(2x² - 7y)(4x⁴ + 14x²y + 49y²).
Step-by-step explanation:
To find the factors of 24x⁶ - 1029y³ , we can use the distributive property of multiplication. The common factor in both terms is 3, so we can factor it out:
24x⁶ - 1029y³ = 3(8x⁶ - 343y³)
Now, we can use the difference of cubes formula to factor 8x⁶ - 343y³:
8x⁶ - 343y³ = (2x² - 7y)(4x⁴ + 14x²y + 49y²).
Therefore, the factors of 24x⁶ - 1029y³ are 3(2x² - 7y)(4x⁴ + 14x²y + 49y²).