Expanding and Factoring: Tips and Tricks for An-1 | Theorem Included

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Discussion Overview

The discussion revolves around the expansion and factoring of the expression \(a^n - 1\). Participants inquire about the methods and theorems applicable to this mathematical expression, focusing on both expansion and factoring techniques.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant seeks assistance on how to expand or factor \(a^n - 1\) and questions if there is a theorem related to this process.
  • Another participant clarifies the expression in question as \(a^n - 1\) rather than \(a^{n-1}\).
  • A later reply provides a formula for factoring \(a^n - 1\) as \((a - 1)(a^{n-1} + a^{n-2} + \cdots + a^2 + a + 1)\), suggesting it is a well-known result.

Areas of Agreement / Disagreement

Participants generally agree on the expression being discussed, but there is no consensus on the methods or theorems applicable beyond the provided formula.

Contextual Notes

The discussion does not address potential limitations or assumptions regarding the use of the formula, nor does it explore the conditions under which it applies.

crazyformath2
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Can someone help me.

How would you expand or factor out an-1

Is there a theorem for this?
 
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is it a^(n-1) or (a^n)-1?
 
(a^n)-1
 
It's a pretty well known formula:

[tex]a^n- 1= (a-1)(a^{n-1}+ a^{n-2}+ \cdot\cdot\cdot+ a^2+ a+ 1)[/tex]
 

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