Question

(iii) (a2 + b2 - c2)2 – (a2 – b2 + c2)2









if answered wrong i will report​

Answer 1

$we \: \: will \: \: use \: \: this \: \: identity \: \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ so \: \: according \: \: to \: \: identity \: \\ ( {a}^{2} + {b}^{2} - {c}^{2} {)}^{2} - ( {a}^{2} - {b}^{2} + {c}^{2} {)}^{2} \\ = ( {a}^{2} + {b}^{2} - {c}^{2} + ( {a}^{2} - {b }^{2} + {c}^{2} ))( {a}^{2} + {b}^{2} - {c}^{2} - ( {a}^{2} - {b}^{2} + {c}^{2} )) \\ = ( {a}^{2} + {b}^{2} - {c}^{2} + {a}^{2} - {b}^{2} + {c}^{2} )( {a}^{2} + {b}^{2} - {c}^{2} - {a}^{2} + {b}^{2} - {c}^{2} ) \\ = (2 {a}^{2} )(2 {b}^{2} - 2 {c}^{2} ) \\ = 2 {a}^{2} (2 {b}^{2} - 2 {c}^{2} ) \\ = 4 {a}^{2} {b}^{2} - 4 {a}^{2} {c}^{2} \: \: \: ans$

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