Once the operator ◊ is defined in the set of real numbers by the relation a ◊ b = ab – a – b, what is the value of the expression (a ◊ b) ◊ c – (a ◊ c) ◊ b?
2b – 2c
a - 2ac
a + bc
2c + ab
b + 2c
answer-2b-2c
hi
(a ◊ b) ◊ c - (a ◊ c) ◊ b
= (ab-a-b) ◊ c - (ac-a-c) ◊ b
= ((ab-a-b)c - (ab-a-b) - c) - ((ac-a-c)b - (ac-a-c) -b)
= abc-ac-bc-ab+a+b-c-(abc-ab-bc-ac+a+c-b)
= abc-ac-bc-ab+a+b-c-abc+ab+bc+ac-a-c+b
=2b-2c
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