Question

Which of the following is a sum of cubes?

Answer 1

Hello!

The answer is:

D) $x^{3}+8y^{6}$

Why?

We are looking for the expression that can be obtained from a sum of cube factoring, the form of the sum of cubes will be:

$a^{3}+b^{3}=(a+b)(a^{2} -ab+b^{2})$

The only option that matches with the sum of cubes form is the last option,

D) $x^{3}+8y^{6}$

and it can be rewritten as the following expression:

$x^{3}+8y^{6}=x^{3}+(2y^{2})^{3}\\\\x^{3}+(2y^{2})^{3}=(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})\\\\(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})=(x+2y^{2})(x^{2}-2xy^{2}+4y^{4})\\\\(x+2y^{2})(x^{2}-xy^{2}+4y^{4})=x*x^{2}-2x^{2}y^{2}+2xy^{4}+2x^{2}y^{2}-2xy^{4}+8y^{6}\\\\x*x^{2}-2x^{2}y^{2}+2xy^{4}+2x^{2}y^{2}-2xy^{4}+8y^{6}=x^{3}+8y^{6}$

Therefore, we have that:

$x^{3}+8y^{6}=x^{3}+(2y^{2})^{3}=(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})=x^{3}+8y^{6}$

Hence, the correct answer is:

D) $x^{3}+8y^{6}$

Have a nice day!

Answer 2

Answer:

D) $x^3+8y^6$

Step-by-step explanation:

We have been given four choices.

A) $3x^3+8y^6$

B) $8x^3-27y^6$

C) $125x^6-9y^3$

D) $x^3+8y^6$

Now we need to find about which of the above choices is a sum of cubes.

Basically we need to check which one of the given choices can be represented in cubic form along with addition sign.

3 and 9 can't be written in cubic form unless we use radical numbers.

So the only choice left is D)

D) $x^3+8y^6$

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

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

which is clearly visible as sum of cubes.