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: \(8x^6+27\)
\(8x^6+27\)
⇒ \((2x^2)^3+(3)^3\)
which is the sum of perfect cube.
Option B: \(x^9+1\)
\(x^9+1\)
⇒ \((x^3)^3+(1)^3\)
which is the sum of perfect cube.
Option C: \(81x^3+16x^6\)
\(81x^3+16x^6\)
⇒ \(9^2x^3+4^2(x^2)^3\)
which is not the sum of perfect cube.
Option D: \(x^6+x^3\)
\(x^6+x^3\)
⇒ \((x^2)^3+x^3\)
which is the sum of perfect cube.
Option E: \(27x^9+x^{12}\)
\(27x^9+x^{12}\)
⇒ \((3x^3)^3+(x^4)^3\)
which is the sum of perfect cube.
Option F: \(9x^3+27x^9\)
⇒ \(3^2x^3+(3x^3)^3\)
which is not the sum of perfect cube.
Option A, B, D, E are the sums of perfect cubes
