(x+2x2)5\left(x + \frac{2}{x^2}\right)^5(x+x22)5
n = 5, r = 4, p = x and q = 2x2\frac{2}{x^2}x22
5C4_{4}4x4^{4}4 (2x2\frac{2}{x^2}x22)1 = 5C4_{4}4 2x4x2\frac{2x^4}{x^2}x22x4
5C4_{4}4 2x2^{2}2 = 5!(5−4)! 4!\frac{5!}{(5-4)!\,4!}(5−4)!4!5! * 2x2^{2}2
5⋅4!4!⋅2x2\frac{5\cdot4!}{4!} \cdot 2x^24!5⋅4!⋅2x2 = 5 * 2x2^{2}2 = 10x2^{2}2
The coefficient is 10.
