Is This Simplified Boolean Expression Correct?

[Kernul]

Homework Statement

Simplify the expression $cb' + ca'b + cabd + cad'$

Homework Equations

All the properties of boolean algebra.

The Attempt at a Solution

Here's how I did it:
$$cb' + ca'b + cabd + cad' = $$
$$c(b' + a'b + abd + ad') = $$
$$c(b' + a'b + a(bd + d')) = $$
$$c((a + a')b' + a'b + a(bd + (b + b')d')) = $$
$$c(ab' + a'b' + a'b + a(bd + bd' + b'd')) = $$
$$c(a(b' + bd + bd' + b'd') + a'b' + a'b) = $$
$$c(a(b'(d + d') + bd + bd' + b'd') + a'b' + a'b) = $$
$$c(a(b'd + bd' + bd + bd' + b'd') + a'b' + a'b) = $$
$$c(a(b'd + bd' + bd + b'd') + a'b' + a'b) = $$
$$c(a(b'(d + d') + bd' + bd) + a'b' + a'b) = $$
$$c(a(b'(d + d') + b(d' + d)) + a'b' + a'b) = $$
$$c(a(b' + b) + a'b' + a'b) = $$
$$c(a + a'b' + a'b) = $$
$$c(a + a'(b' + b)) = $$
$$c(a + a') = $$
$$c$$
Is all this correct? Was there a better and faster way to do it?

 

[berkeman]

Have you checked your answer using a Karnaugh Map? That's a good way for you to check your answers in Boolean algebra manipulations.

(Hint -- I think you'll like what you find in your K-map)

 

[ehild]

It looks correct. Remember the identity A+A'B=A+B. It is very useful!