(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Well, I was trying to expand say for the third power of (A+B), where A and B are non-commutative.

3. The attempt at a solution

I get

[tex] (A+B)^3=(A^2+AB+BA+B^2)(A+B)=A^3+ABA+BA^2+B^2A+A^2B+AB^2+BAB+B^3[/tex]

but from a few sources online, it should be

[tex] (A+B)^3=(A^3+3A^2B+3AB^2+B^3)-3(AB-BA)(A+B) [/tex]

Now, these 2 results don't seem to be equivalent and I have checked this by expanding it myself. I have been thinking for quite some time about what is wrong with my answer but I seem to be getting nowhere. Any help would be greatly appreciated.

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# Homework Help: Non-commutative Binomial

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