Answer:
Option (a) is correct.
[tex]-27a^3b^6+8a^9b^{12}[/tex] can be represented as the sum of cubes as [tex](-3ab^2)^3+(2a^3b^4)^3[/tex]
Step-by-step explanation:
Given : Some expression.
We have to choose an expression from the given options that represents the sum of cubes.
An expression can be represented as the sum of cubes when it can be written in form of [tex](ax)^3+(by)^3[/tex]
That is the expression can be written in some power of 3.
Consider
[tex]-27a^3b^6+8a^9b^{12}[/tex]
Since, 27 can be written as [tex]3^3[/tex]
And [tex]a^3b^6[/tex] can be written as [tex](ab^2)^3[/tex]
Also, 8 can be written as [tex]2^3[/tex]
And [tex]a^9b^{12}[/tex] can be written as [tex](a^3b^4)^3[/tex]
Thus, [tex]-27a^3b^6+8a^9b^{12}[/tex] can be written as [tex](-3ab^2)^3+(2a^3b^4)^3[/tex]
Thus, [tex]-27a^3b^6+8a^9b^{12}[/tex] can be represented as the sum of cubes as [tex](-3ab^2)^3+(2a^3b^4)^3[/tex]
