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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

1 Answer

4 votes

Answer

C. 27x⁹+y⁶


Step-by-step 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.

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