Factorize x³-x-y+y³ perfectly

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Mohamedhany

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Mar 16, 2020
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Hello! Iam having trouble factorizing this question. I tried to find a solution using an app on the internet. But the solution required considering x³-x-y+y³ as a polynomial over x. And I have no idea what that means. Can anyone help me solve this with a simple solution that is not complicated.
 
Hello, and welcome to FMH! :)

I would group as follows:

[MATH](x^3+y^3)-(x+y)[/MATH]
Can you proceed?
 
Mohamedhany said:
Hello! Iam having trouble factorizing this question. I tried to find a solution using an app on the internet. But the solution required considering x³-x-y+y³ as a polynomial over x. And I have no idea what that means. Can anyone help me solve this with a simple solution that is not complicated.
Click to expand...
Considering the expression as a polynomial over x just means thinking of x as the only variable, and y as a mere parameter (constant). So you would think of it as x^3 - x + (y^3 - y), with (y^3 - y) treated as a single number.

But I don't see how that would help, since cubics are not nice to factor in general. I would do exactly as MarkFL did.

If you want to understand what the app said, you'll have to show us what it said, in its entirety. I suspect, however, that it did something a human would never do!
 
Dr.Peterson said:
Considering the expression as a polynomial over x just means thinking of x as the only variable, and y as a mere parameter (constant). So you would think of it as x^3 - x + (y^3 - y), with (y^3 - y) treated as a single number.

But I don't see how that would help, since cubics are not nice to factor in general. I would do exactly as MarkFL did.

If you want to understand what the app said, you'll have to show us what it said, in its entirety. I suspect, however, that it did something a human would never do!
Click to expand...
Thank you for your help. I was scratching my head on what does considering an expression as a polynomial meant.
 
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