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 [tex]a^3+b^3[/tex].
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.
[tex]27x^9+y^6[/tex]
We can rewrite our expression by writing terms as cubes:
[tex]3^3\cdot ( x^3)^3+(y^2)^3[/tex]
[tex]( 3x^3)^3+(y^2)^3[/tex]
Therefore, expression [tex]27x^9+y^6[/tex] is a sum of cubes.
In 4th expression, we can see that [tex]81=9^2=3^4[/tex]. We cannot represent it as a cube. Similarly, we cannot represent [tex]y^{40}[/tex] as a cube. Therefore, 4th expression is not correct.
