Using Binomial theorem, expand \( (a+b)^{4} \). Hence or otherwise ...

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Using Binomial theorem, expand \( (a+b)^{4} \). Hence or otherwise prove that
\[
(1-x)^{8}=(1-2 x)^{4}+4 x^{2}(1-2 x)^{3}+6 x^{4}(1-2 x)^{2}+4 x^{6}(1-2 x)+x^{8} .
\]
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