Trying to simplify the following boolean expression but suck and new to this

Question

Expression:

$[x + (yz)](x' + z)$

My attempt:

1. $[x + (yz)](x' + z)$
2. $(x + y)(x + z)(x' + z) \quad \textit{Distributive law}$

The answer is supposed to be: $(x + y) \times z$

N.B. I am still new to this and learning, I am using the following book:

Discrete Mathematics for Computing / Edition 3
by Peter Grossman

Answer 1

• $ [x+(yz)](x′+z) $ distributiv law =>
• $ (x+y)(x+z)(x′+z) $ commutative law =>
• $ (x+y)(z+x)(z+x') $ distributive law =>
• $ (x+y)(z+(xx')) $ complement Law =>
• $ (x+y)(z+0) $ identity law =>
• $ (x+y)z $

(Laws From: Laws of Boolean Algebra (electronics-tutorials.ws))