# Basic question about distribution

Would $(a \otimes b + c \otimes d) \Delta \otimes Id = \Delta(a) \otimes b + \Delta(c) \otimes d$?

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### 2 comments

1. I guess you mean $\Delta \otimes Id (a \otimes b + c \otimes d) = \Delta(a) \otimes b + \Delta(c) \otimes d$.
Let me return the question to (any of) you: why would that be true?

2. allahandrow

The reason it’s true is because we extend linearly.

To see an example of this during the lectures and in the notes is when Federico presented the Sweedler notation for the coassociativity law.