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Câu hỏi: Khai triển \({\left( {3x + 1} \right)^{10}}\) cho tới x3.
Lời giải chi tiết
Ta có:
\(\eqalign{
& {\left({3x + 1} \right)^{10}} = {\left({1 + 3x} \right)^{10}}\cr& = \sum\limits_{k = 0}^{10} {C_{10}^k{{. 1}^{10 - k}}{{\left({3x} \right)}^k}} \cr&= \sum\limits_{k = 0}^{10} {C_{10}^k{{\left({3x} \right)}^k}} \cr&= 1 + C_{10}^1\left({3x} \right) + C_{10}^2{{\left({3x} \right)}^2} + C_{10}^3{{\left({3x} \right)}^3} + ... \cr
& = 1 + 30x + 405{x^2} + 3240{x^3} + ... \cr} \)
Ta có:
\(\eqalign{
& {\left({3x + 1} \right)^{10}} = {\left({1 + 3x} \right)^{10}}\cr& = \sum\limits_{k = 0}^{10} {C_{10}^k{{. 1}^{10 - k}}{{\left({3x} \right)}^k}} \cr&= \sum\limits_{k = 0}^{10} {C_{10}^k{{\left({3x} \right)}^k}} \cr&= 1 + C_{10}^1\left({3x} \right) + C_{10}^2{{\left({3x} \right)}^2} + C_{10}^3{{\left({3x} \right)}^3} + ... \cr
& = 1 + 30x + 405{x^2} + 3240{x^3} + ... \cr} \)