3

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.

Sakib Arifin
  • 151
Haggra
  • 223

1 Answers1

5

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.

amWhy
  • 209,954
  • Please explain further. That much was obvious from the question. – Haggra Nov 02 '16 at 19:38
  • Suppose we have $xy = a$, $x' = b$, and $z = c$. Then $F=(xy)+(x'z)= a+(bc)$, In turn by distribution of addition over a product, we have $(a+b)(a+c) = (xy+x')(xy+z)$. – amWhy Nov 02 '16 at 19:42
  • I appreciate your help, and your philosophy of being patient and nice you wrote in your profile. Stackoverflow also needs people like you. Have a good day or evening, whatever the time is over there. – Haggra Nov 02 '16 at 19:47
  • Glad to help, Haggra! – amWhy Nov 02 '16 at 19:47