Question

Which are sums of perfect cubes? Check all that apply. 8x6 27 x9 1 81x3 16x6 x6 x3 27x9 x12 9x3 27x9.

Answer 1

Answer:

A,B,D,E

Step-by-step explanation:

Got it right on the assignment

Answer 2

The equations which are sums of perfect cubes are as follows;

$\rm 8x^6+27x^9+1$

$\rm x^6+x^3$

$\rm 27x^9+x^{12}$

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 $\rm 8x^6+27x^9+1$.

The equation can be written as;

$\rm 8x^6+27x^9+1\\\\2^3(x^2)^3+3^3(x^3)^3+1^3$

All the terms in the expression are can be represented as perfect cubes.

2.  The given equation is $\rm 81x^3+16x^6$.

The equation can be written as;

$\rm 81x^3+16x^6\\\\9^2x^3+4^2(x^2)3$

In this, all the terms are not perfect cubes, some of them are squares.

3. The given equation is $\rm x^6+x^3$.

The equation can be written as;

$\rm x^6+x^3\\\\(x^2)^3+x^3$

All the terms in the expression are perfect cubes.

4.  The given equation is $\rm 27x^9+x^{12}$.

The equation can be written as;

$\rm 27x^9+x^{12}\\\\3^3(x^3)^3+(x^4)^3$

All the terms in the expression are perfect cubes.

5.   The given equation is $\rm 9x^3+27x^9$.

The equation can be written as;

$\rm 9x^3+27x^9\\\\3^2x^3+3^3(x^3)^3$

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.

brainly.com/question/4701925