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Disclaimer: Doesn't work with TraditionalForm

list = Table[PolynomialQuotient[x^n - a^n, x - a, x], {n, 2, 12}]; ClearAttributes[{Plus, Times}, Orderless] list /.   Plus[a{h_[a, x] :> Plus[xh[x, a] /. Times[a, x] :> Times[x, a] /.   t : Times[Power[a, i_], Power[x, j_]] :> Times[Power[x, j], Power[aReverse@t, i]] /.   t : Times[a, Power[x, j_]] :> Times[Power[x, j]Reverse@t, a] /.   t : Times[Power[a, i_], x] :> Times[x, Power[a, i]]Reverse@t} /.   Plus[a : Plus[Power[aPower[a, i_], m__b__, c : Power[x, j_]] :> Plus[Power[x, j], mPlus[c, Power[ab, i]]a] // Column  

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Don't forget

SetAttributes[{Plus, Times}, Orderless] 

Disclaimer: Doesn't work with TraditionalForm

list = Table[PolynomialQuotient[x^n - a^n, x - a, x], {n, 2, 12}]; ClearAttributes[{Plus, Times}, Orderless] list /.   Plus[a, x] :> Plus[x, a] /. Times[a, x] :> Times[x, a] /.   Times[Power[a, i_], Power[x, j_]] :> Times[Power[x, j], Power[a, i]] /.   Times[a, Power[x, j_]] :> Times[Power[x, j], a] /.   Times[Power[a, i_], x] :> Times[x, Power[a, i]] /.   Plus[Power[a, i_], m__, Power[x, j_]] :> Plus[Power[x, j], m, Power[a, i]] // Column 

enter image description here

Don't forget

SetAttributes[{Plus, Times}, Orderless] 

Disclaimer: Doesn't work with TraditionalForm

list = Table[PolynomialQuotient[x^n - a^n, x - a, x], {n, 2, 12}]; ClearAttributes[{Plus, Times}, Orderless] list /. {h_[a, x] :> h[x, a], t : Times[Power[a, i_], Power[x, j_]] :> Reverse@t, t : Times[a, Power[x, j_]] :> Reverse@t, t : Times[Power[a, i_], x] :> Reverse@t} /. Plus[a : Power[a, i_], b__, c : Power[x, j_]] :> Plus[c, b, a] // Column  

enter image description here

Don't forget

SetAttributes[{Plus, Times}, Orderless] 
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Source Link
eldo
  • 84.7k
  • 6
  • 94
  • 210

Disclaimer: Doesn't work with TraditionalForm

list = Table[PolynomialQuotient[x^n - a^n, x - a, x], {n, 2, 12}]; ClearAttributes[{Plus, Times}, Orderless] list /. Plus[a, x] :> Plus[x, a] /. Times[a, x] :> Times[x, a] /. Times[Power[a, i_], Power[x, j_]] :> Times[Power[x, j], Power[a, i]] /. Times[a, Power[x, j_]] :> Times[Power[x, j], a] /. Times[Power[a, i_], x] :> Times[x, Power[a, i]] /. Plus[Power[a, i_], m__, Power[x, j_]] :> Plus[Power[x, j], m, Power[a, i]] // Column 

enter image description here

Don't forget

SetAttributes[{Plus, Times}, Orderless] 
list = Table[PolynomialQuotient[x^n - a^n, x - a, x], {n, 2, 12}]; ClearAttributes[{Plus, Times}, Orderless] list /. Plus[a, x] :> Plus[x, a] /. Times[a, x] :> Times[x, a] /. Times[Power[a, i_], Power[x, j_]] :> Times[Power[x, j], Power[a, i]] /. Times[a, Power[x, j_]] :> Times[Power[x, j], a] /. Times[Power[a, i_], x] :> Times[x, Power[a, i]] /. Plus[Power[a, i_], m__, Power[x, j_]] :> Plus[Power[x, j], m, Power[a, i]] // Column 

enter image description here

Don't forget

SetAttributes[{Plus, Times}, Orderless] 

Disclaimer: Doesn't work with TraditionalForm

list = Table[PolynomialQuotient[x^n - a^n, x - a, x], {n, 2, 12}]; ClearAttributes[{Plus, Times}, Orderless] list /. Plus[a, x] :> Plus[x, a] /. Times[a, x] :> Times[x, a] /. Times[Power[a, i_], Power[x, j_]] :> Times[Power[x, j], Power[a, i]] /. Times[a, Power[x, j_]] :> Times[Power[x, j], a] /. Times[Power[a, i_], x] :> Times[x, Power[a, i]] /. Plus[Power[a, i_], m__, Power[x, j_]] :> Plus[Power[x, j], m, Power[a, i]] // Column 

enter image description here

Don't forget

SetAttributes[{Plus, Times}, Orderless] 
Source Link
eldo
  • 84.7k
  • 6
  • 94
  • 210

list = Table[PolynomialQuotient[x^n - a^n, x - a, x], {n, 2, 12}]; ClearAttributes[{Plus, Times}, Orderless] list /. Plus[a, x] :> Plus[x, a] /. Times[a, x] :> Times[x, a] /. Times[Power[a, i_], Power[x, j_]] :> Times[Power[x, j], Power[a, i]] /. Times[a, Power[x, j_]] :> Times[Power[x, j], a] /. Times[Power[a, i_], x] :> Times[x, Power[a, i]] /. Plus[Power[a, i_], m__, Power[x, j_]] :> Plus[Power[x, j], m, Power[a, i]] // Column 

enter image description here

Don't forget

SetAttributes[{Plus, Times}, Orderless]