Simplify ( a+b)( a - b)+ (b + c) ( b - c) + ( c + a) ( c - a)
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& = AB + A'C + BC \\
& = AB + A'C + BC(A+A') \\
& = AB + A'C + ABC + A'BC \\
& = AB + ABC + A'C + A'BC \\
& = AB (1 + C) + A'C (1 + B) \\
& = AB + A'C
\end{align}
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