How to Correctly Simplify This Boolean Expression?

[torx11]

Homework Statement

Simplify the following
xyz + x'(w+z') + yz(w+z')

Homework Equations

The Attempt at a Solution

xyz + x'(w + z') + yz(w + z')
xyz + x'w + x'z' + yz(w + z')
xyz + x'w + x'z' + yzw + yzz'
xyz + x'w + x'z' + yzw + 0

I got the answer xyz + x'w + x'z' + yzw

However in the book it says the answer is xyz + x'w + x'z'. How could that be? I don't see any way of getting rid of yzw. Please tell me if this is correct or I need to fix something. Thank you.

 

[vela]

If y=z=w=1, just the first three terms will evaluate to 1, regardless of what x equals, so yzw is apparently hidden in there.

Use xyz + x'w + x'z' + yzw = xyz + x'w + x'z' + yzw(x+x'). Multiply the last term out and then simplify.