Khai triển (1 + 2x)^10 = a0 + a1x + a2x^2 + … + a10x^10. Tìm a7.
Khai triển (1 + 2x)10 = a0 + a1x + a2x2 + … + a10x10. Tìm a7.
Lời giải
Xét khai triển: \({\left( {1 + 2x} \right)^{10}} = \sum\limits_{k = 0}^{10} {C_{10}^k\,.\,{2^k}\,.\,{x^k}} \)
\( = C_{10}^0\,.\,{2^0}\,.\,{x^0} + C_{10}^1\,.\,{2^1}\,.\,{x^1} + C_{10}^2\,.\,{2^2}\,.\,{x^2} + ... + C_{10}^{10}\,.\,{2^{10}}\,.\,{x^{10}}\)
\[ \Rightarrow {a_7} = C_{10}^7\,.\,{2^7} = 15\,\,360\].