help on simplifying boolean algebra

Question

I need t show the the terms on the left simplify to the ones on the right $$(X+Y).(X'+Z)= X.Z+X'.Y$$

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My attempt:

I went with $$XX'+XZ+YX'+YZ= 0 +XZ+YX'+YZ$$

But I'm stumped beyond this point, any help would be much appreciated

Answer 1

Hint: $YZ = YZ(X+X') \\ = XYZ+X'YZ$

Hint 2: Absorption $A+AB = A$

Answer 2

In boolean algebra if $A=B$ then $AC=BC$
Now let's consider your equation $$(X+Y).(X'+Z)=XZ+YX'+YZ \tag{1.}$$ this has to be proved equal to $$XZ+X'Y \tag{2.}$$ Now multiply both eq (1.) and (2.) by $Z'$ you will get both equal to $X'YZ'$