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SMO 2025 Open Round 1 Question 19

SMO · SMO 2025 Open Round 1

Question 19

Find $a_9$ if for all real values of $x$, we have
$$(2x+1)^{20}=(x+1)^{10}(a_0+a_1x+a_2x^2+\ldots+a_{10}x^{10})+b_0+b_1x+b_2x^2+\ldots+b_9x^9.$$