HW3 Q4 clarification

I started doing number 4 and I’m a bit confused by it. We have that xy=qyx and when I did the example for (x+y)^2 I got

(x+y)^2 = x^2 + xy + yx + y^2 = x^2 + qyx + yx + y^2 = x^2 + (q+1)yx + y^2

and when I used the formula I got that

\sum_{i=0}^{2}\binom{2}{k}x^{k}y^{2-k}=x^2 + (q+1)xy + y^2. What’s tripping me out are the middle terms of these expressions because if what we want to show holds then

(q+1)yx=(q+1)xy \iff qyx+yx=qxy+xy \iff xy+yx=qxy+xy \implies yx=qxy but we are not told that yx=qxy. I’m not sure if i’m tired and this is obvious or if xy=qyx is a typo and it should actually be yx=qxy because then the equality of the middle terms is clear. 

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5 comments

  1. Servando, you’re right. It is a typo; the equation should read yx = qxy.

  2. rafael11112013

    Hello, I also wanted to ask something. In 4b) it says to generalize it to the multinomial case. Does it mean that we just give a formula or we also need to give a formula and prove it?

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