Answer:
Option A, B, D, E are the sums of perfect cubes
Step-by-step explanation:
Given some choices we have to select the option which are the sums of perfect cubes.
Option A: [tex]8x^6+27[/tex]
[tex]8x^6+27[/tex]
⇒ [tex](2x^2)^3+(3)^3[/tex]
which is the sum of perfect cube.
Option B: [tex]x^9+1[/tex]
[tex]x^9+1[/tex]
⇒ [tex](x^3)^3+(1)^3[/tex]
which is the sum of perfect cube.
Option C: [tex]81x^3+16x^6[/tex]
[tex]81x^3+16x^6[/tex]
⇒ [tex]9^2x^3+4^2(x^2)^3[/tex]
which is not the sum of perfect cube.
Option D: [tex]x^6+x^3[/tex]
[tex]x^6+x^3[/tex]
⇒ [tex](x^2)^3+x^3[/tex]
which is the sum of perfect cube.
Option E: [tex]27x^9+x^{12}[/tex]
[tex]27x^9+x^{12}[/tex]
⇒ [tex](3x^3)^3+(x^4)^3[/tex]
which is the sum of perfect cube.
Option F: [tex]9x^3+27x^9[/tex]
⇒ [tex]3^2x^3+(3x^3)^3[/tex]
which is not the sum of perfect cube.
Option A, B, D, E are the sums of perfect cubes
