Question

Which are sums of perfect cubes? Check all that apply.

A=8x6 + 27
B=x9 + 1
C=81x3 + 16x6
D=x6 + x3
E=27x9 + x12
F=9x3 + 27x9

Answer 1

a b d e

hope that helped :)

Answer 2

Option A, B, D, E are the sums of perfect cubes

Explanation:

Given some choices we have to select the option which are the sums of perfect cubes.

Option A:
`8x^6+27`

`8x^6+27`

⇒
`(2x^2)^3+(3)^3`

which is the sum of perfect cube.

Option B:
`x^9+1`

`x^9+1`

⇒
`(x^3)^3+(1)^3`

which is the sum of perfect cube.

Option C:
`81x^3+16x^6`

`81x^3+16x^6`

⇒
`9^2x^3+4^2(x^2)^3`

which is not the sum of perfect cube.

Option D:
`x^6+x^3`

`x^6+x^3`

⇒
`(x^2)^3+x^3`

which is the sum of perfect cube.

Option E:
`27x^9+x^(12)`

`27x^9+x^(12)`

⇒
`(3x^3)^3+(x^4)^3`

which is the sum of perfect cube.

Option F:
`9x^3+27x^9`

⇒
`3^2x^3+(3x^3)^3`

which is not the sum of perfect cube.

Option A, B, D, E are the sums of perfect cubes