Вправи: 119

119. Доведіть тотожність:

bca-b(a-c) + acb-a(b-c) + abc-a(c-b) = 1;

bc\b-ca-b(a-c) + ac\a-cb-a(b-c) + ab\a-ba-c(b-c) = bcb-c- aca-c+ ab(a-b)a-ba-c(b-c) = b2c-bc2- a2c+ac2+a2b+abc-abca-ba-c(b-c) = a2b- a2c-abc+ac2- (ab2- abc- b2c+bc2)a-ba-c(b-c) = aab-ac-bc+ c2- b(ab-ac-bc+ c2)a-ba-c(b-c) = a-b(ab-ac-bc+ c2)a-ba-c(b-c) = a-b(ab-c- cb-c)a-ba-c(b-c) = a-ba-c(b-c)a-ba-c(b-c) = 1.