How to simplify this Boolean expression

Question

F=(A+B+C)(A+B+C')(A+B'+C')

I used sop method and I am left with A+BC', so the above expression should leave me with (A+B)(A+C'). Iam not able to get to this answer. Help is appreciated.

Answer 1

$$\begin{align} F & =(\color{blue}{A+B}+\color{red}{C})(\color{blue}{A+B}+\color{red}{C'})(A+B'+C')\tag{1}\\ & = ((\color{blue}{A+B})+(\color{red}{CC'}))(A + B' + C')\tag{2}\\ & =(\color{green}{A}+B)(\color{green}{A}+B'+C')\tag{3}\\ & = \color{green}{A}+(B(B'+C'))\tag{4} \\ & = A+ \underbrace{BB'}_{\large = \, 0} + BC' \tag{5}\\ & = A + BC' \tag{6 SOP} \\ & = (A+B)(A+C')\tag{7 POS} \end{align}$$

Answer 2

$\begin{align} F & =(A+B+C)(A+B+C')(A+B'+C') \\ & = (A+B+C)\Bigl((A+B+C')(A+B+C')\Bigr)(A+B'+C') \\ & = \Bigl((A+B+C)(A+B+C')\Bigr)\Bigl((A+B+C')(A+B'+C')\Bigr) \\ & = (A+B)(A+C') \\ & = A+AB+AC'+BC' \\ & = A + BC' \end{align}$