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Sum of the factors of 4b²c² – (b² + c² – a²)² is :
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- a + b + c
- 2(a + b + c)
- 0
- 1
Correct Option: B
4b²c² – (b² + c² – a²)²
= (2bc)² – (b² + c² – a²)²
= (2bc + b² + c² –a²) (2bc – b² – c² + a²)
= {(b + c)² – a²} {a² – (b² + c² – 2bc)}
= (b + c + a) (b + c – a) {a² – (b–c)²}
= (b + c + a) (b + c – a) (a + b – c) (a – b + c)
∴ Required sum
= b + c + a + b + c – a + a + b – c + a – b + c
= 2 (a + b + c)
