How is $X+X'Y = X+Y$?

Question

I have been searching online and the answer I am getting is not making sense to me.

My professor wrote on the board: $$X+X'Y = (X+X')(X+Y) = X+Y.$$

But I am not understanding where is he getting $(X+X')(X+Y)$ from?

I know that $(X+X') = 1$ so $1*(X+Y) = X+Y. $

The picture attached is the list of all the Duality Principle we are using.

Answer 1

Hint:

Apply $(T8')~~X+Y\cdot Z=(X+Y)\cdot(X+Z)$ on $X+X'\cdot Y$ see what you get.