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

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Can I make this general statement?

A^{n}(B+C)^{n} = (AB+AC)^{n}?
 
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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?

A^{n}(B+C)^{n} = (AB+AC)^{n}?

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.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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