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!
First of all, this is a math question.

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
$$(x \cdot 1) + (x \cdot y) = 
  x \cdot (1 + y) =
  x \cdot 1 = x.$$