Đáp án:
Giải thích các bước giải:
\[\begin{array}{l}
{(1 - 3x + {x^2})^{10}} = \sum\limits_{k = 0}^{10} {C_{10}^k} {x^{2(10 - k)}}{(1 - 3x)^k} = \sum\limits_{k = 0}^{10} {C_{10}^k} {x^{20 - 2k}}.\sum\limits_{l = 0}^l {C_k^l} {( - 3x)^l}{.1^{k - l}} = \sum\limits_{k = 0}^{10} {C_{10}^k} .\sum\limits_{l = 0}^l {C_k^l} .{x^{20 - 2k + l}}.{( - 3)^l}(0 \le l \le k \le 10)\\
{x^8} \Rightarrow \left\{ \begin{array}{l}
20 - 2k + l = 8\\
0 \le l \le k \le 10
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
(k;l) = (10;8)\\
(k;l) = (9;6)\\
(k;l) = (8;4)\\
(k;l) = (7;2)\\
(k;l) = (6;0)
\end{array} \right.\\
\Rightarrow He\_so\_{x^8} = C_{10}^{10}.C_{10}^8.{( - 3)^8} + ... + C_{10}^6.C_6^0.{( - 3)^0} = 1185645\\
\end{array}\]
