Factor X^6+8: Solution & Explanation

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The discussion focuses on factoring the expression X^6 + 8, with the solution provided as (x^2 + 2)(x^4 - 2x^2 + 4). Participants explore the connection to the formula for factoring a sum of cubes, recognizing that X^6 can be expressed as (x^2)^3 and 8 as 2^3. The confusion arises around identifying the correct values for a and b, which are determined to be a = x^2 and b = 2. Ultimately, the explanation clarifies the factorization process, leading to a better understanding of the solution. The thread concludes with a participant expressing gratitude for the clarification.
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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
 
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Nitrate said:

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?
 
Dick said:
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
 
Nitrate said:
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?
 
Dick said:
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 :)
 

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