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Câu 21 trang 67 SGK Đại số và Giải tích 11 Nâng cao

Khai triển
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Đề bài

Khai triển \({\left( {3x + 1} \right)^{10}}\) cho tới x3.

Lời giải chi tiết

Ta có:

\(\eqalign{
& {\left( {3x + 1} \right)^{10}}  = {\left( {1 + 3x} \right)^{10}}\cr& = \sum\limits_{k = 0}^{10} {C_{10}^k{{.1}^{10 - k}}{{\left( {3x} \right)}^k}} \cr&= \sum\limits_{k = 0}^{10} {C_{10}^k{{\left( {3x} \right)}^k}} \cr&= 1 + C_{10}^1\left( {3x} \right) + C_{10}^2{{\left( {3x} \right)}^2} + C_{10}^3{{\left( {3x} \right)}^3} + ... \cr 
ཧ& = 1 + 30x + 405{x^2} + 3240{x^3} + ... \cr} \)

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