Question

Which expression is a sum of cubes?

Answer 1

It's C, 27x^9+y6

hope this helps!

Answer 2

We have been given 4 expressions. We are asked to choose the expression that represents sum of cubes.

We know that sum of cubes is in form $a^3+b^3$.

We can see that 1st and 2nd option has a negative sign. Therefore, these options cannot be sum of cubes.

Let us check 3rd and 4th options one by one.

$27x^9+y^6$

We can rewrite our expression by writing terms as cubes:

$3^3\cdot ( x^3)^3+(y^2)^3$

$( 3x^3)^3+(y^2)^3$

Therefore, expression $27x^9+y^6$ is a sum of cubes.

In 4th expression, we can see that $81=9^2=3^4$. We cannot represent it as a cube. Similarly, we cannot represent $y^{40}$ as a cube. Therefore, 4th expression is not correct.