Prove Identity by Algebraic Manipulations

Question

Question 1: (A + C)(A' + B)(B + C) = BC

Sol: using left hand side:-

Please help me solving it furhter

Answer 1

Hint: $\rm BC = (A + A')BC = ABC+A'BC$

So from where you left off: $$\begin{align}\rm AB+\color{blue}{BC}+A'C ~=~&\rm BC \\ \rm AB+\color{blue}{ABC+A'BC}+A'C ~=~&\rm BC \\ \vdots~~~&\end{align}$$

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Or, alternatively

$$\begin{align}\rm AB+BC+A'C ~=~&\rm \color{blue}{BC} \\ \rm AB+BC+A'C~=~&\rm \color{blue}{BC+BC} \\ \rm AB+BC+A'C ~=~&\rm \color{blue}{ABC+A'BC+BC} \\ \vdots~~~&\end{align}$$