Question

Which expression is a sum of cubes?

A. -27a^3b^6+8a^9b^12

B. -9a^3b^6+a^9b^10

C. 9a^3b^6+8a^9b^12

D. 27a^3b^6+8a^9b^12

Answer 1

Answer: -27a^3 b^6 + 8a^9 b^12 is the right answer

Explanation:

I got a 100% on the quiz

Answer 2

Answer:A.
`-27a^3b^6+8a^9b^(12)`

D.
`27a^3b^6+8a^9b^(12)`

Explanation:

A.
`-27a^3b^6+8a^9b^(12)`

which is equivalent to

`(-3)^3a^3(b^2)^3+2^3(a^3)^3(b^4)^3\\=(-3ab^2)^3+(2a^3b^4)^3`

This expression is a sum of cubes.

B.
`-9a^3b^6+a^9b^(10)`

Here 9 is not a perfect cube and power of b in second term is 10 which is not a multiple of 3 , thus this cannot be written as sum of cubes.

C.
`9a^3b^6+8a^9b^(12)`

Here 9 is not a perfect cube. Thus this cannot be written as sum of cubes.

D.
`27a^3b^6+8a^9b^(12)\\=3^3a^3(b^2)^3+2^3(a^3)^3(b^4)^3\\=(3ab^2)^3+(2a^3b^4)^3`

This expression is a sum of cubes.