Final answer:
The expression that is a sum of cubes is option d. 64x⁶y¹² + 125x⁹y³. To determine which expression is a sum of cubes, we need to look for the pattern (a³ + b³). In option d, we have 64x⁶y¹² (which is equal to (4x²)³) and 125x⁹y³ (which is equal to (5xy)³). Therefore, option d is a sum of cubes.
Step-by-step explanation:
The expression that is a sum of cubes is option d. 64x⁶y¹² + 125x⁹y³.
To determine which expression is a sum of cubes, we need to look for the pattern (a³ + b³). In option d, we have 64x⁶y¹² (which is equal to (4x²)³) and 125x⁹y³ (which is equal to (5xy)³). Therefore, option d is a sum of cubes.
As a general rule, a sum of cubes can be represented as (a³ + b³) = (a + b)(a² - ab + b²).