I was doing this one boolean algebra problem and I don\'t know if I am doing it

Question

I was doing this one boolean algebra problem and I don't know if I am doing it right or wrong.

The question is this:

Simplify the following expressions by applying one of the theorems. State the theorems used:

(a'b + cd') (a'b+ce)

What I did was going to use the Distributive Law: X +YZ = (X + Y) (X+Z)

I set the following:
X = a'b
Y = cd'
Z = ce

Thus, I get a'b + ( cd' ce )

Since I went from (X + Y) (X + Z) to X + YZ is this simplifying it at all? Or should I been looking at the problem a different way and using a different theorem/law?

Thanks

Explanation / Answer

Yes, you did that part correctly, but you can simplify again. a'b + (cd')(ce) = a'b + c(d'e) c anded with itself is c You now are using less logic gates than when you started.

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