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Câu 60 trang 94 SGK Đại số và Giải tích 11 Nâng cao

Tìm hệ số
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Đề bài

Tìm hệ số của \({x^8}{y^9}\) trong khai triển của \({\left( {3x + 2y} \right)^{17}}\)

Lời giải chi tiết

Ta có:  \({\left( {3x + 2y} \right)^{17}} = \sum\limits_{k = 0}^{17} {C_{17}^k{{\left( {3x} \right)}^{17 - k}}{{\left( {2y} \right)}^k}} \)\( = \sum\limits_{k = 0}^{17} {C_{17}^k{3^{17 - k}}{{.2}^k}.{x^{17 - k}}{y^k}} \)Hệ số của số hạng chứa \({x^8}{y^9}\) (ứng với \(k = 9\)) là \(C_{17}^9{3^8}{2^9}\)

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