Simplifying this boolean function How can I completely simplify this equation using algebraic simplification rules?

$$x'y'z + x'yz + xyz$$
We use the distributive law twice:

$$\begin{align} x'y'z + x'yz + xyz &amp; = x'z(\underbrace{y' + y}_{= 1}) + xyz \\ \\ &amp; = x'z + xyz \\ \\ &amp;= z(x' + xy)\end{align}$$

What counts as simplified depends on the context.
We can further simplify by the distributive property:

$$z(x' + xy)=z((x'+x)(x'+y))=z(x'+y)$$
where $x'+x$ is always true.

Check out:
http://en.wikipedia.org/wiki/Boolean_algebra_(structure)#Definition