<s>[INST] Simplify $(A+C)(AD+AD) + AC + C$ using Boolean algebra I have solved the equation like this:
 (A + C)(AD + AD) + AC + C
=(A + C)(AD) + (A + C)(AD) + AC + C
=AAD + ACD + AAD + ACD + AC + C
=AAD + AAD + ACD + ACD + AC + C
=AAD + ACD + AC + C 
=AAD + ACD + C(A+1)
=AAD + ACD + C
=AD + ACD + C
=AD(1+C) + C
=AD + C

Am I right? 
 [/INST] I would have taken the following steps:
$$
\begin{align}
   (A + C)(AD + AD) + AC + C
&= (A + C)(AD) + (AC + C)\\
&= AD + ADC + C\\
&= AD + C\\
\end{align}
$$
</s>