<s>[INST] Commutativity and $(a + b)^2$ I read "note that if a and b are commutative, $(a + b)^2 = a^2 + 2ab + b^2$".
Could someone explain how we need commutativity for this to happen?
 [/INST] Expand it termwise: 
$$(a+b)^2 = (a+b) \cdot (a+b) = a \cdot a + \color{blue}{a \cdot b} + \color{red}{b \cdot a} + b\cdot b$$
Commutativity assures us that $a\cdot b = b\cdot a$ so that the expression becomes 
$$(a+b)^2 = a^2 + 2ab + b^2$$
Without commutativity, we have to leave our answer as it is in the first expression, we cannot simplify it to the second expression. 
</s>