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What is the purpose of the brackets in all the examples I've seen of the distributive law? Why are there no brackets when distributing an AND term and there are when distributing an OR term? Could I write:

X * (Y + Z) = (X * Y) + (X * Z)?

eg of law. X * (Y + Z) = X * Y + X * Z
X + (Y * Z) = (X + Y) * (X + Z)

Note: I'm very new to boolean algebra

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The order of operations is * then +. So $X * Y + X * Z$ means $(X * Y) + (X * Z)$ but $X + Y * X + Z$ means $X + (Y * X) + Z$. That is why the parentheses are necessary in these statements of the laws: $$X * (Y + Z) = X * Y + X * Z$$ $$X + Y * Z = (X + Y) * (X + Z)$$ Sometimes we put in extra parentheses to emphasize the order of operations, as in $$X * (Y + Z) = (X * Y) + (X * Z)$$ $$X + (Y * Z) = (X + Y) * (X + Z)$$

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