Question

simplify (7a-6b+5c)²+(7a+6b-5c)²​

Answer 1

Answer:

$(a - b + c) { }^{2} + (a + b - c) { }^{2}$

Answer 2

Answer:

Let us expand the given expression:

(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)}]

By using the formula,

(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

∴ (7a – 6b + 5c)2 + (7a + 6b – 5c)2 = 98a2 + 72b2 + 50c2 – 120bc