Is this a Boolean Algebra Theorem/Law?

Question

I just wanted to ask if this law is correct?

(X'+Y)(X+Z) = X'Z + XY

I saw it from this picture

number 16 http://image.slidesharecdn.com/booleanalgebralaws-121126060037-phpapp02/95/boolean-algebra-laws-1-638.jpg?cb=1353931281

And When I foil it out, this is what I get.

(X'+Y)(X+Z) = X'X + X'Z + XY + YZ

= X'Z + XY + YZ

Which does not equal the law above

Answer 1

I change my answer:

These equations are equivalent:

(X'+Y)(X+Z) = X'Z + XY
X'X + X'Z + XY + YZ = X'Z + XY     (expand left hand)
X'Z + XY + YZ = X'Z + XY           (X'X = 0 always)
X'Z + XY = X'Z + XY                (YZ => X'Z + XY)

The last step can be seen like this. There are two possibilities:

1. YZ=1

   Then both Y=1 and Z=1, and then the right hand of the equation is also 1 (given that at least X=1 or X'=1).

2. YZ=0

   The term can thus be removed from the equation, and then both hands are equal.

NB: you might get better replies on maths.exchange for these types of questions.