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I began to use Mathematica a few days. My problem is: How to expand expression like $(a+b)*(a+b)$, where this multiplication is non commutative? Mathematica can do this?

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Maybe Distribute[(a + b) ** (a + b) ] ? – b.gatessucks Apr 10 '13 at 17:02
Look here for some more thoughts about non commutative multiplication and more ... – Spawn1701D Apr 10 '13 at 18:08
up vote 6 down vote accepted

Distribute[] is a useful thing:

Distribute[(a + b) ** (c + d)]
   a ** c + a ** d + b ** c + b ** d
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