If \( A \) be the sum of the odd terms and \( B \) the sum of the even terms in the expansion of...

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If \( A \) be the sum of the odd terms and \( B \) the sum of the even terms in the expansion of \( (x+a)^{n} \), prove that \( A^{2}-B^{2}=\left(x^{2}-a^{2}\right)^{n} \).
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