Đáp án:
\(6600\)
Giải thích các bước giải:
\(\begin{array}{l}
x{\left( {1 - 2x} \right)^5} = x\sum\limits_{k = 0}^5 {C_5^k.{{\left( { - 2} \right)}^k}{x^k}} = \sum\limits_{k = 0}^5 {C_5^k.{{\left( { - 2} \right)}^k}{x^{k + 1}}} \\
\Rightarrow k + 1 = 5 \Rightarrow k = 4\\
\Rightarrow \,he\,so\,cua\,{x^5}\,la\,\,C_5^4.{\left( { - 2} \right)^4}\\
{x^2}{\left( {1 + 3x} \right)^{10}} = {x^2}\sum\limits_{{k_1} = 0}^{10} {C_{10}^{{k_1}}{{.3}^{{k_1}}}{x^{{k_1}}}} = \sum\limits_{{k_1} = 0}^{10} {C_{10}^{{k_1}}{{.3}^{{k_1}}}{x^{{k_1} + 2}}} \\
\Rightarrow {k_1} + 2 = 5 \Rightarrow {k_1} = 3\\
\Rightarrow \,he\,so\,cua\,{x^5}\,la\,\,C_{10}^3{.3^3}\\
\Rightarrow \,he\,so\,cua\,{x^5}\,trong\,P\,la\,\,C_5^4.{\left( { - 2} \right)^4} + C_{10}^3{.3^3} = 6600
\end{array}\)
