Respuesta :
The equations which are sums of perfect cubes are as follows;
[tex]\rm 8x^6+27x^9+1[/tex]
[tex]\rm x^6+x^3[/tex]
[tex]\rm 27x^9+x^{12}[/tex]
Perfect cubes;
Perfect cubes are the numbers that are the triple product of the same number.
We have to determine
Which are sums of perfect cubes?
1. The given equation is [tex]\rm 8x^6+27x^9+1[/tex].
The equation can be written as;
[tex]\rm 8x^6+27x^9+1\\\\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.
2. The given equation is [tex]\rm 81x^3+16x^6[/tex].
The equation can be written as;
[tex]\rm 81x^3+16x^6\\\\9^2x^3+4^2(x^2)3[/tex]
In this, all the terms are not perfect cubes, some of them are squares.
3. The given equation is [tex]\rm x^6+x^3[/tex].
The equation can be written as;
[tex]\rm x^6+x^3\\\\(x^2)^3+x^3[/tex]
All the terms in the expression are perfect cubes.
4. The given equation is [tex]\rm 27x^9+x^{12}[/tex].
The equation can be written as;
[tex]\rm 27x^9+x^{12}\\\\3^3(x^3)^3+(x^4)^3[/tex]
All the terms in the expression are perfect cubes.
5. The given equation is [tex]\rm 9x^3+27x^9[/tex].
The equation can be written as;
[tex]\rm 9x^3+27x^9\\\\3^2x^3+3^3(x^3)^3[/tex]
In this, all the terms are not perfect cubes, some of them are squares too.
To know more about perfect cubes click the link given below.
https://brainly.com/question/4701925
Answer:
A,B,D,E
Step-by-step explanation:
Got it right on the assignment
