Which expression is a sum of cubes?
a.-24a^15+125b^18
b.-64a^27+b^8
c.27x^9+y^6
d.81x^24+8y^40

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.