Proof on discrete maths, help :)

I 'm trying to proove that :

(a AND -b) OR (b AND -c) OR (c AND -a) = (a OR b OR c) AND (-a OR -b OR -c)

i ve put it on truth table and its working, but i have to do it actually without truth table, so i tryed boolean algebra.

I think that i am making a fatal mistake but i dont know where it is. So i started from this with boolean algebra --> (a OR b OR c)AND(-a OR -b OR -c) trying to reach 1st part, but actually this is what i achived :

aa' + ab' + ac' + ba' +bb' +bc' + ca' + cb' + cc' =

ab' + ac' + ba' +bc' + ca' +cb' =

(a XOR c) + (b XOR c) + (a XOR b)

+ = logical OR

multiplies = logical AND

Thanks in advance for your help :)