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

READ :  If    a2+b2+4c2 = ab+2bc+2ca | Expansion - Algebra

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