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

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

1 Like