Question

prove that |ā+b|^2-|ā-b|^2=4ā.b​

Answer 1

Ques. : Prove that -

${(a + b)}^{2} \: - {(a - b)}^{2} = 4ab$

Sol. :

${(a + b)}^{2} \: - {(a - b)}^{2}$

= $( {a}^{2} + 2ab + {b}^{2} ) - ( {a}^{2} - 2ab + {b}^{2} )$

= ${a}^{2} + 2ab + {b}^{2} \: - {a}^{2} + 2ab - {b}^{2}$

= $4ab$

------ (PROVED)

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