Which expression is a sum of cubes?

-27a3b6+8a9b12

-9ab6 + 9610

9ab6 + 8a12

27a3b8+8a9b12

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

Step-by-step explanation:

We are to determine which of the expression above in the options satisfy sum of a cube.

For an expression to considered sum of a cube, it must meet two conditions:

1) the expression would have same sign. It is mostly positive. If both are negative, the negative sign could be factored out.

2) Each of the term in the expression must be a cube. That is, each term must be the result of multiplying the same expression three times.

Let's check out the expressions in the options:

a) - 27a^3b^6+8a^9b^12

The two terms in the expression have opposite signs

b) - 9ab^6 + 9610

The two terms in the expression havd opposite signs

c) 9ab^6 + 8a^12

The two terms in the expression have same signs. But 9ab^6 isn't a cube as we can't multiply a tern 3times to derive it, but 8a^12 is a cube.

d) 27a^3b^8+8a^9b^12

The two terms in the expression have same signs (positive). 27a^3b^8 is a cube, 8a^9b^12 is also a cube

27a³b^8 = 3ab² * 3ab² * 3ab²

8a^9b^12 = 2a³b⁴ * 2a³b⁴ * 2a³b⁴

From the options above 27a^3b^8+8a^9b^12 is sum of a cube