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} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ac }

= [ 49a^{2} + 36b^{2} + 25c^{2}+{ – 84ab } +{– 60bc } + { 70ac } ] + [ 49a^{2} + 36b^{2} + 25c^{2} +{84ab } + { - 60bc} +{– 70ac } ]

= [ 49a^{2} + 36b^{2} + 25c^{2} – 84ab – 60bc + 70ac ] + [ 49a^{2} + 36b^{2} + 25c^{2} + 84ab – 60bc – 70ac ]

= 49a^{2} + 36b^{2} + 25c^{2} – 84ab – 60bc + 70ac + 49a^{2} + 36b^{2} + 25c^{2} + 84ab – 60bc – 70ac

= 98a^{2} + 72b^{2} + 50c^{2} – 120bc

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