Question

What should be added to 4c(– a + b + c) to obtain 3a(a + b + c) – 2b(a – b + c)?

Answer 1

Let x be added to the given expression

4c(– a + b + c) to obtain 3a(a + b + c) – 2b(a – b + c)

i.e. x + 4c(– a + b + c) = 3a(a + b + c) – 2b(a – b + c)

⇒ x = 3a(a + b + c) – 2b(a – b + c) – 4c(– a + b + c)

= 3a² + 3ab + 3ac – 2ba + 2b² – 2bc + 4ca – 4cb – 4c²

⇒ x = 3a² + ab + 7ac + 2b² – 6bc – 4c²  ...[Adding the like terms]