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\[(x^{3}+1)\]

mmhm!

no, (x+1)(x^2-x+1)

\[(a + b)^3 = (a + b)(a^2 - ab + b^2)\]

\[(x+1)(x^{2}-x+1)\]

That's the sum of cubes formula I posted above.

ya basically what they said

ok but I just established that (x^3+1) and (x+1)^3 weren't the same thing :S

right, so then how can I use the sum of cubes formula? b/c isn't that for (a+b)3

Because
\((x^3 + 1) = (x^3 + 1^3)\)

Remember, \(1 = 1 \times 1 \times 1 = 1^3 \)

= (x + 1) ^3 ?? but wouldnt that make it the same??

No, I just explained to you earlier that \((x^3 + 1) \ne (x + 1)^3\)

\((x^3 + 1) = (x^3 + 1^3)\)
\((x + 1)^3 = (x + 1)(x + 1)(x + 1)\)

ok, so (a^3 + b^3) doesn't equal (a+b)^3, ever right? Sorry, just trying to wrap my head around it

The only way is if x = 0 or x = 1

But in general, they will not be equal

and the answer is x=17 and x = -1

so how do I get from the sum of cubes to -1

What I say doesn't matter if you don't understand anything.

The silence is deafening

Oh goodie :D