Question

Which are sums of perfect cubes? Check all that apply. 8x6 + 27 x9 + 1 81x3 + 16x6 x6 + x3 27x9 + x12 9x3 + 27x9

Answer 1

(A) 8x^6+27

(B) x^9+1

(D) x^6+3

(E) 27x^9+x^12

Explanation:

:)

Answer 2

Sums of perfect cubes are

• 
  `8x^6 + 27x^9 + 1`

• 
  `x^6 + x^3`

• 
  `27x^9 + x^(12)`

Explanation:

Option (1)
`8x^6 + 27x^9 + 1`

This can be written as

`2^3 (x^2)^3 + 3^3(x^3)^3 +1^3`

All the terms in the expression are can be represented as perfect cubes

Option (2)
`81x^3 + 16x^6`

This can be written as

`9^2 x^3 + 4^2 (x^2)^3`

In this , all the terms are not perfect cubes , some of them are squares

Option (3)
`x^6 + x^3`

This can be written as

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

All the terms in the expression are perfect cubes

Option (4)
`27x^9 + x^(12)`

This can be written as

`3^3(x^3)^3 + (x^(4))^3`

All the terms in the expression are perfect cubes

Option (5)
`9x^3 + 27x^9`

This can be written as

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

In this , all the terms are not perfect cubes , some of them are squares too