Factoring difference of squares not working?

[Marin12]

Homework Statement

If $(x+1)(x-1)=3$, what is $(x^3-x)(x^3+x)$?

Relevant Equations

$(a-b) (a+b) =a^2-b$

Why factoring difference of squares does not always work?
For example
$(x^3 - x)(x^3 + x) = x^6 - x^2$
but if I factor x^2 out from both I get $(x^2(x-1))(x^2(x+1))$ which is $x^4(x^2 -1)=x^6 - x^4$

Are there any rules I am not aware of?
Tried using chat gpt and searching the web, but no success.

Any help is welcomed, thank you in advance

 

[WWGD]

Homework Statement: If $(x+1)(x-1)=3$, what is $(x^3-x)(x^3+x)$?
Relevant Equations: $(a-b) (a+b) =a^2-b$

Why factoring difference of squares does not always work?
For example
$(x^3 - x)(x^3 + x) = x^6 - x^2$
but if I factor x^2 out from both I get $(x^2(x-1))(x^2(x+1))$ which is $x^4(x^2 -1)=x^6 - x^4$

Are there any rules I am not aware of?
Tried using chat gpt and searching the web, but no success.

Any help is welcomed, thank you in advance

Check when you do the factoring, e.g.
$x^2(x-1)$. Does it equal $x^3-x$?

 

[Marin12]

omg.. i feel embarased, no words. thank you very much

 

[neilparker62]

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