Вправи: 832

832. Доведіть тотожність:

1) 1a2+ 12a+36 + 236- a2 + 1a2- 12a+36 = 1\(a-6)2(a+6)2–2\a-6(a+6)a-6(a+6) + 1\(a+6)2(a-6)2 = (a-6)2-2a-6a+6+ (a+6)2(a+6)2(a-6)2 = (a-6-(a-6))2(a2- 36)2 = (a-6-a+6)2(a2- 36)2 = 122(a2- 36)2 = 144(a2- 36)2.

2) a2a-b(a-c) + b2b-a(b-c) + c2c-a(c-b) = a2\b-ca-b(b-c) – b2\a-ca-b(b-c) + c2\a-bc-a(b-c) = a2b-c- b2a-c+ c2(a-b)a-ba-c(b-c) = a2b- a2c- b2a+ b2c+ c2a- c2ba-ba-c(b-c) = a2b- a2c- b2a+ b2c+ c2a- c2ba2b- a2c-abc+ac2- ab2+ abc+ b2c-bc2 = a2b- a2c- b2a+ b2c+ c2a- c2ba2b- a2c- b2a+ b2c+ c2a- c2b = 1.