Question

Which expression is a sum of cubes?

-24a^15+125b^18
-64a^27+b^a
-27x^9+y^6
-81x^24+8y^40

Answer 1

`-27x^9+y^6 = (-3)^3* \Big(x^3\Big)^3 + \Big(y^2\Big)^3=\boxed{\Big(-3x^3\Big)^3+\Big(y^2\Big)^3}`

Answer 2

Option (3) is correct.

`-27x^9+y^6` is the expression written as the sum of cubes as

`(-3x^3)^3+(y^2)^3`

Explanation:

Sum of cubes : is defined as
`a^3+b^3`

We have to choose a sum of cubes from given expressions,

Consider
`-27x^9+y^6`

Here
`-27x^9` can be written as
`(-3x^3)^3`

and
`y^6` can be written as
`(y^2)^3`

Thus,
`-27x^9+y^6=(-3x^3)^3+(y^2)^3`

Hence,
`-27x^9+y^6` is the expression written as the sum of cubes as
`(-3x^3)^3+(y^2)^3`

Thus, option (3) is correct.