Confirmation on boolean expression simplifications

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This is expression no.1: $(A+B’)\cdot C + A \cdot C $.

So i think these are the simplification steps: $$(A+B’)\cdot C + A \cdot C = A\cdot C + B' \cdot C + A \cdot C = B' \cdot C + A \cdot C => C \cdot(A + B')$$

And this is expression no.2: $(A + B’ + C’)\cdot(A’ + B’ + C’)\cdot(A’ + B’ + C’)$.

So i think these are the simplification steps: $$(A + B’ + C’)\cdot(A’ + B’ + C’)\cdot(A’ + B’ + C’) = (A + B’ + C’)\cdot(A’ + B’ + C’) = (B' + C')\cdot (B' + C') => (B' + C') $$

Are these simplifications correct?