Boolean Algebra : proving $ a + b (c + a') = a + b $

Question

How to prove that $ a + b (c + a') = a + b $? ($a'$ is not $a$)

I can see that this expression is valid by using a truth table, but I would like to prove it by using only algebra expressions. Any leads?

Answer 1

Notice these rules (or identities) $$1+X = 1, \qquad X + YX = (1+Y)X = X, \qquad X+X' = 1$$

Then \begin{align}a + b(a'+c) &= (a + ba) + b(a'+c)\\ &= a+b(a+a'+c) \\&= a+b\end{align}