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Giải bài 2.24 trang 37 Chuyên đề học tập Toán 10 – Kết nối tri thức

Tìm hệ số của \({x^9}\) trong khai triển thành đa thức của \({\left( {2x - 3} \right)^{11}}\)

♛Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

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Đề bài

Tìm hệ số của \({x^9}\) trong khai triển thành đa thức của \({\left( {2x - 3} \right)^{11}}\)

Phương pháp giải - Xem chi tiết

Số hạng chứa \({x^k}\) trong khai triển của \({(ax + b)^n}\) là \(C_n^{n - k}{(ax)^k}{b^{n - k}}\) Do đó hệ số của \({x^k}\) trong khai triển của \({(ax + b)^n}\) là \(C_n^{n - k}{a^k}{b^{n - k}}\)

Lời giải chi tiết

Số hạng chứa \({x^k}\) trong khai triển của \({\left( {2x - 3} \right)^{11}}\) là \(C_{11}^{11 - k}{(2x)^k}{( - 3)^{11 - k}}\)Số hạng chứa \({x^9}\) ứng với \(k = 9\), tức là số hạng \(C_{11}^2{(2x)^9}{( - 3)^2}\) hay \(253440{x^9}\)Vậy hệ số của \({x^9}\) trong khai triển của \({\left( {2x - 3} \right)^{11}}\) là \(253440.\)

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