I am given a function $F$ such that:
$$F = xy + x'z$$
In a solution of an example, the following is done. I am trying to understand how the author deduced this result. Only thing explained is that distribution law was used.
$$F = xy + x'z = (xy + x')(xy + z)$$
I do not know which steps or operations are made, the book assumes that it is a simple step because there are no intermediate steps, thus I assume that I'm missing something simple.
Can you explain what's being done here and what are the intermediate steps? If there is a simple rule to deduce it in one step, please provide a proof.
It is, indeed, using the distributive property:
$$F = \color{blue}{xy} + \color{red}{x'z} = (\color{blue}{xy} + \color{red}{x'})(\color{blue}{xy} + \color{red}{z})$$
What I did was to distribute $xy$ and sum it with $x'$, also with $z$. Since $x'z$ is a product, the distribution results, too, as a product.