Solving General Arithmatic: A^{n}(B+C)^{n} = (AB+AC)^{n}

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Homework Help Overview

The discussion revolves around the expression A^{n}(B+C)^{n} and its potential equivalence to (AB+AC)^{n}, exploring whether this holds true in a general context, particularly focusing on the nature of A, B, and C.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the validity of the general statement and discussing the conditions under which it might hold, including the nature of the variables involved (matrices vs. polynomials) and the commutativity of A and B+C.

Discussion Status

The conversation is exploring different interpretations of the expression, with some participants suggesting that the commutativity of the terms is a necessary condition for the rearrangement, while others clarify the context of the variables as polynomials rather than matrices.

Contextual Notes

There is an ongoing discussion about the assumptions regarding the types of mathematical objects involved (matrices vs. polynomials) and their properties, particularly regarding commutativity.

Titans86
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Can I make this general statement?

[tex]A^{n}(B+C)^{n} = (AB+AC)^{n}[/tex]?
 
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You're comfortable that (ab)^n = (a^n)(b^n) (aside from a few restrictions) correct? Is there anything you can do to change your expression into the form (a^n)(b^n)?
 
Titans86 said:
Can I make this general statement?

[tex]A^{n}(B+C)^{n} = (AB+AC)^{n}[/tex]?

If those are matrices, do you think you might need that A and B+C commute to make that rearrangement?
 
Last edited:
not matrices but polynomials...
 
They commute. So you should be fine.
 

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