Answer
C. 27x⁹+y⁶
Explanation
We have to test all the expressions
A.-24a^15+125b^18 = -24a¹⁵+5³b¹⁸
= -24(a⁵)³ + (5b⁶)³
-24a^15+125b^18 ⇒ Is an expression of sum of cubes.
B.-64a^27+b^8 = -4³a²⁷+b⁸
= (4a⁹)³ + b⁸
Not a sum of cubes since 8 is not divisible by 3.
C. 27x^9+y^6 = 3³x⁹+y⁶
= (3x³)³ + (y²)³
27x^9+y^6 ⇒ Is an expression of sum of cubes.
D. 81x^24+8y^40 = 81x²⁴+8y⁴⁰
= 81(x⁸)³ + 2³y⁴⁰
81x^24+8y^40 ⇒ Is an not expression of sum of cubes.
