# Associativity Question

Can someone step by step the last line? Confused.

• It looks like there is an error to me. The "$z$" term should be "$y$" instead, shouldn't it? And I think there is more than associativity being used here. – MPW Jul 28 '17 at 13:37
• I added the previous 2 lines. What else is being used? – JiHua Jul 28 '17 at 13:42
• Well, commutativity for one. Going from line two to line three, you should be able to quickly verify that the left-hand-sides are the same, it just changes $(x+y\times z)$ out for $(y\times z + x)$. The right hand sides on the other hand, you can think of it first as unwrapping all of the parentheses, rearranging, and rewrapping. $\color{blue}{x\times z}+((\color{red}{y\times z} + \color{green}{x})+\color{purple}{y}) = (\color{blue}{x\times z} + \color{green}{x})+(\color{red}{y\times z} + \underbrace{\color{purple}{y}})$. They made the mistake of switching purple $y$ for $z$ instead. – JMoravitz Jul 28 '17 at 14:04