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Using the binomial theorem (without usin...

Using the binomial theorem (without using the formula for `.^(n)C_(r)`), prove that
`.^(n)C_(4)+.^(m)C_(2)-.^(m)C_(1).^(n)C_(2)=.^(m)C_(4)-.^(m+n)C_(1).^(m)C_(3)+.^(m+n)C_(2).^(m)C_(2)-.^(m+n)C_(3).^(m)C_(1)+.^(m+n)C_(4)`.

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