How can I find the coefficient of x when the power is greater than the powers of 2 brackets using binomial expansion? I have been given this question:
Find the coefficient of $x^{13}$ in the expansion of $(1 + 2x)^4(2 + x)^{10}$.
I know how I would find $x^4$ or lower degrees, but I am unsure how to approach this, as neither term has a $x^{13}$, and x is a prime number so it can't just be 2 terms multiplied (as neither bracket has a power of 13).
Where do I start with this?
 This is revision rather than homework, but hints would be appreciated.

If you expand the two terms, the first one will give you terms from $1$ to $16x^4$.  The second will give you terms from $2^{10}$ to $x^{10}$.  When you multiply them, the only two ways to get $x^{13}$ is to use the $x^3$ term from the first and the $x^{10}$ term from the second or to use the $x^4$ from the first and the $x^9$ from the second.  Evaluate the coefficients of each of these terms, multiply, and add.
