Having trouble with simplifying in Boolean algebra

Question

I want to solve this problem:

$$(x . y . z + x . y + x)$$

Which turns into this when you group $x$

$$x . ( yz + y + 1 ) $$

What I don't understand is why is there a "1" at the end? Does the last $x $ turn into a 1? If so, why?

My math book is unclear, I'm having a hard time.

Answer 1

If you look at the equation,

$x.y.z+x.y+x$

$=x.y.z+x.y+x.1$

This is basic boolean algebra, $[a.1=a]$ $[a+1=1]$

So if you group $x$,$1$ will be left at the end,as boolean algebra follow Distributive law.

Answer 2

You should use the identity rule for the last x before using the distributive rule.