Factor X^6+8: Solution & Explanation

[Nitrate]

Homework Statement

Factor
X^6+8

Homework Equations

The answer: (x^2 + 2)(x^4 - 2x^2 + 4)

The Attempt at a Solution

I'm really not sure how to arrive at the answer. Although, I have a feeling that I have to use (a + b)(a^2 - ab + b^2) because the question looks looks similar to a^3 + b^3

 

[Dick]

Homework Statement

Factor
X^6+8

Homework Equations

The answer: (x^2 + 2)(x^4 - 2x^2 + 4)

The Attempt at a Solution

I'm really not sure how to arrive at the answer. Although, I have a feeling that I have to use (a + b)(a^2 - ab + b^2) because the question looks looks similar to a^3 + b^3

You've already got it. If a^3+b^3=x^6+8, what should a and b be?

 

[Nitrate]

You've already got it. If a^3+b^3=x^6+8, what should a and b be?

I suppose this is where I'm stuck.

a= x^2
b= 2

?
I'm still a bit confused on how we got a = x^2

 

[Dick]

I suppose this is where I'm stuck.

a= x^2
b= 2

?
I'm still a bit confused on how we got a = x^2

You want a^3 to equal x^6, right? You don't see why (x^2)^3=x^6?

 

[Nitrate]

You want a^3 to equal x^6, right? You don't see why (x^2)^3=x^6?

I see it now.
Thank you :)