I have trouble solving this problem:
Find the coefficient of $x^3y^4$ in $(x+2y+3)^{10}$
The reason for that I struggle with this problem, is because it has an higher order (10) the $x^3y^4$.
In the solution, he has made this $(x+2y+3)^{10}$ to this -> $(7x+2y)^7$. But I don't understand how he did that?
The terms of the development will be of the form $$\frac{10!}{i!j!k!}x^i(2y)^j3^k \quad\text{ with } \ i+j+k=10$$
With $i=3$ and $j=4$ this leaves $k=3$. So it's $$\frac{10!}{3!4!3!}x^3(2y)^43^3$$ which means the coefficient of $x^3y^4$ is equal to $$\frac{10!}{3!4!3!}2^4\cdot 3^3$$
(Compilation of comments by Yves Daoust and Hanne.)