Express the following as a sum of perfect square | 16a2 + b2 + 9c2 – 4ab – 3bc – 12ca

  Express the following as a sum of perfect square:
    16a² + b² + 9c² – 4ab – 3bc – 12ca

=1/2.(2.16a² + 2. b² + 2. 9c² – 8ab – 6bc – 24ca)
= 1/2.(16a² + 16a²+ b² + b² + 9c² + 9c² – 8ab – 6bc – 24ca)
= 1/2.(16a² – 8ab + b² + b² – 6bc + 9c² + 16a² – 24ca + 9c²)
= 1/2.{(16a² – 8ab + b² ) + ( b² – 6bc + 9c²) + ( 16a² – 24ca + 9c²)}
= 1/2.{(16a² – 2.4a.b + b² ) + ( b² – 2.b.3c + 9c²) + ( 16a² – 2.4a.3c + 9c²)}
= 1/2.{(4a – b)² + ( b-3c )² + ( 4a-3c )²} Answer