Q. 2 C4.0( 13 Votes )

Simplify

(7a – 6b + 5c)2 +(7a + 6b – 5c)2

Answer :

(7a – 6b + 5c)2 +(7a + 6b 5c)2 = [(7a)2 +(- 6b)2 +(5c)2 +{2 ×(7a)×(- 6b)} +{2 ×(- 6b)× (5c)} +{2 ×(7a)×(5c)} ] + [(7a)2 +(6b)2 +(- 5c)2 +{2 ×(7a)×(6b)} +{2 ×(6b)× (- 5c)} +{2 ×(7a)×(-5c)} ]


{ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac }


= [ 49a2 + 36b2 + 25c2+{ – 84ab } +{– 60bc } + { 70ac } ] + [ 49a2 + 36b2 + 25c2 +{84ab } + { - 60bc} +{– 70ac } ]


= [ 49a2 + 36b2 + 25c2 – 84ab – 60bc + 70ac ] + [ 49a2 + 36b2 + 25c2 + 84ab – 60bc – 70ac ]


= 49a2 + 36b2 + 25c2 – 84ab – 60bc + 70ac + 49a2 + 36b2 + 25c2 + 84ab – 60bc – 70ac


= 98a2 + 72b2 + 50c2 – 120bc


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