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:

Sums of perfect cubes are

• $8x^6 + 27x^9 + 1$

• $x^6 + x^3$

• $27x^9 + x^{12}$

Step-by-step explanation:

Option (1) $8x^6 + 27x^9 + 1$

This can be written as

$2^3 (x^2)^3 + 3^3(x^3)^3 +1^3$

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

Option (2) $81x^3 + 16x^6$

This can be written as

$9^2 x^3 + 4^2 (x^2)^3$

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

Option (3) $x^6 + x^3$

This can be written as

$(x^2)^3 + x^3$

All the terms in the expression are  perfect cubes

Option (4) $27x^9 + x^{12}$

This can be written as

$3^3(x^3)^3 + (x^{4})^3$

All the terms in the expression are  perfect cubes

Option (5) $9x^3 + 27x^9$

This can be written as

$3^2x^3 + 3^3(x^3)^3$

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

Answer 2

Answer:

(A) 8x^6+27

(B) x^9+1

(D) x^6+3

(E) 27x^9+x^12

Step-by-step explanation:

:)