Question

Which expression is a sum of cubes?

Answer 1

Answer:A. $-27a^3b^6+8a^9b^{12}$

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

Step-by-step 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.