<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] It looks just fine! Well done!
A bit more simply, $$\begin{align}(A+C)(AD+AD)+AC+C &= (A+C)AD+AC+C\\ &= AAD+CAD+AC+C\\ &= AD+(AD+A+1)C\\ &= AD+C\end{align}$$
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