I have been stuck for a while trying to solve this, but it feels incomplete.
We first consider the distributivity and therefore start by proving that
$$a ∨ (b ∧ c) ╞ (a∨b)∧(a∨c)$$
Supose that for a value we have
$$a ∨ (b ∧ c) = True$$
$$a = True$$ or $$(b∧c) = True $$
Here I would make the jump to the right side of the equation, but I am unsure on how to concretely do it.
Also I am only proving this for one side of the equation, I will then have to do the oposite side and a similar proof for the other Distributive Law so a concrete answer would be nice.