# Absorption Law Proof by Algebra

I'm struggling to understand the absorption law proof and I hope maybe you could help me out.

The absorption law states that: $X + XY = X$
Which is equivalent to $(X \cdot 1) + (XY) = X$

No problem yet, it's this next step that stumps me. How can I apply the distributive law when there are two "brackets"?

How can I manipulate $(X \cdot 1) + (XY) = X$ to give me $X \cdot (1+Y)$?

I understand that the absorption law works. I would just like to see how the algebra proof works.

Thank you!

I think you are confused on how brackets are used. They indicate precedence of operations, and can be used anywhere, even in places where such indication is not necessary. For example, $$3 \times 5 + 8$$ and $$(3 \times 5) + 8$$ are both legitimate expressions and they mean exactly the same thing.
Your expression $$(x \cdot 1) + (x \cdot y)$$ is exactly the same as $$x \cdot 1 + x \cdot y.$$ So we may calculate $$(x \cdot 1) + (x \cdot y) = x \cdot (1 + y) = x \cdot 1 = x.$$
Apply the distributive law on $$x\land(1\lor y)$$ and see what you get.