`text{Ta có công thức}`
`(a + b + c)^{n}`
`= sum_{0 ≤ i ≤ k ≤ n}.C_{n}^{k}.C_{k}^{i}.a^{n - k}.b^{k - i}.c^{i}`
`text{Qua đó, nên}`
`(2 + x + x^2)^{5}`
`= sum_{0 ≤ i ≤ k ≤ 5}.C_{5}^{k}.C_{k}^{i}.2^{10 - k}.x^{k - i}.x^{2i}`
`= sum_{0 ≤ i ≤ k ≤ 5}.C_{5}^{k}.C_{k}^{i}.2^{10 - k}.x^{k + i}`
`text{Theo giả thuyết}`
`-> k + i = 5`
`-> (k; i) = {(3; 2); (4; 1)}`
`-> text{Hệ số chứa}` `x^{5}` `text{là}`
`C_{5}^{3}.C_{3}^{2} + C_{5}^{4}.C_{4}^{1} = 50`