Answer:
Sums of perfect cubes are
- [tex]8x^6 + 27x^9 + 1[/tex]
- [tex]27x^9 + x^{12}[/tex]
Step-by-step explanation:
Option (1) [tex]8x^6 + 27x^9 + 1[/tex]
This can be written as
[tex]2^3 (x^2)^3 + 3^3(x^3)^3 +1^3[/tex]
All the terms in the expression are can be represented as perfect cubes
Option (2) [tex]81x^3 + 16x^6[/tex]
This can be written as
[tex]9^2 x^3 + 4^2 (x^2)^3[/tex]
In this , all the terms are not perfect cubes , some of them are squares
Option (3) [tex]x^6 + x^3[/tex]
This can be written as
[tex](x^2)^3 + x^3[/tex]
All the terms in the expression are perfect cubes
Option (4) [tex]27x^9 + x^{12}[/tex]
This can be written as
[tex]3^3(x^3)^3 + (x^{4})^3[/tex]
All the terms in the expression are perfect cubes
Option (5) [tex]9x^3 + 27x^9[/tex]
This can be written as
[tex]3^2x^3 + 3^3(x^3)^3[/tex]
In this , all the terms are not perfect cubes , some of them are squares too
