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Which expression is a sum of cubes?

a. -64x⁶y¹² + 125x¹⁶y³
b. -32x⁶y¹² + 125x¹⁶y³
c. 32x⁶y¹² + 125x⁹y³
d. 64x⁶y¹² + 125x⁹y³

User Pmorken
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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).

User Vovanium
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