Question

Simplify:

(7a – 6b + 5c)² + (7a + 6b – 5c)²

Answer 1

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

= 98a² + 72b² + 50c² – 120bc