Question

Which expression is a sum of cubes?

O-27ab6 +8a9b12
-9a3b6 +8810
O 9a3b6 +8a9b12
27a368 + 8a612

Answer 1

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

Explanation:

In the picture attached, the problem is shown.

A polynomial in the form x³ + y³ is called a sum of cubes

If we take the expression:

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

and take cubic root to each term, we get:

`x = \sqrt[3]{-27 a^3 b^6}`

`x =\sqrt[3]{-27} \sqrt[3]{a^3} \sqrt[3]{b^6}`

`x = -3 a b^2`

`y = \sqrt[3]{8 a^9 b^(12)}`

`y =\sqrt[3]{8} \sqrt[3]{a^9} \sqrt[3]{b^(12)}`

`y =2 a^3 b^4`

The other options are not sum of cubes because 9, -9, b^10 and b^8 are not a perfect cubes.