Binomial Practice

Algebra Level pending

For r= 0,1......,10 let \( A_{r},B_{r},C_{r}\) denote respectively the coefficients of \( x^r\) in the expansions of \( (1+x)^{10},(1+x)^{20}\) and \((1+x)^{30}\) then ; \( \displaystyle \sum_{r=1} ^{10} A_{r}(B_{10}B_{r} - C_{10}A_{r}) \) is :

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