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