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If a + b – c = 0 then the value of 2b2c2 + 2c2a2 + 2a2b2 – a4 – b4 – c4
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- 7
- 0
- 14
- 28
- 7
Correct Option: B
Expression = 2b2c2 + 2c2a2 + 2a2b2 - a4 - b4 - c4
Expression = 4b2c2 - (2b2c2 - 2c2a2 - 2a2b2 + a4 + b4 + c4)
Expression = (2bc)2 - (a2 - b2 - c2)2
Expression = (2bc + a2 - b2 - c2)(2bc - a2 + b2 + c2)
Expression = {a2 - (b2 + c2 - 2bc){(b2 + c2 + 2bc) - a2}
Expression = { a2 - (b - c)2 }{ (b + c)2 - a2 }
Expression = (a – b + c) (a + b – c)(a + b + c) (b + c – a)
If a + b – c = 0,
∴ Expression = 0
