Express the following as a sum of perfect square:

16a^{2} + b^{2} + 9c^{2} – 4ab – 3bc – 12ca

=1/2.(2.16a^{2} + 2. b^{2} + 2. 9c^{2} – 8ab – 6bc – 24ca)

= 1/2.(16a^{2} + 16a^{2}+ b^{2} + b^{2} + 9c^{2} + 9c^{2} – 8ab – 6bc – 24ca)

= 1/2.(16a^{2} – 8ab + b^{2} + b^{2} – 6bc + 9c^{2} + 16a^{2} – 24ca + 9c^{2})

= 1/2.{(16a^{2} – 8ab + b^{2} ) + ( b^{2} – 6bc + 9c^{2}) + ( 16a^{2} – 24ca + 9c^{2})}

= 1/2.{(16a^{2} – 2.4a.b + b^{2} ) + ( b^{2} – 2.b.3c + 9c^{2}) + ( 16a^{2} – 2.4a.3c + 9c^{2})}

= 1/2.{(4a – b)^{2} + ( b-3c )^{2} + ( 4a-3c )^{2}} __Answer__